4

.\- Interrelations

Between

Cement & Concrete

Properties

PART

y ^- ^ 3^/

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
Announcing —The Building Science Series

The "Building Science Series" disseminates technical information developed at the Bureau on building materials, components, systems, and whole structures. The

series presents research results, test methods, and performance criteria related to the

structural and environmental functions and the durability and safety characteristics

of building elements and systems.

These publications, similar in style and content to the NBS Building Materials

and Structure Reports (1938-59), are directed toward the manufacturing, design,

and construction segments of the building industry, standards organizations, offi- cials responsible for building codes, and scientists and engineers concerned with the

properties of building materials.

The material for this series originates principally in the Building Research Division of the NBS Institute for Applied Technology. Published or in preparation

are:

BSSl. Building Research at the National Bureau of Standards. (In preparation.)

BSS2. Interrelations Between Cement and Concrete Properties : Part 1, Materials

and Techniques, Water Requirements and Trace Elements. 35 cents. BSS3. Doors as Barriers to Fire and Smoke. 15 cents. BSS4. Weather Resistance of Porcelain Enamels: Effect of Exposure Site and

Other Variables After Seven Years. 20 cents. BSS5. Interrelations Between Cement and Concrete Properties: Part 2, Sulfate

Expansion, Heat of Hydration, and Autoclave Expansion. 35 cents. BSS6. Some Properties of the Calcium Aluminoferrite Hydrates. 20 cents. BSS7. Organic Coatings—Properties, Selection, and Use. $2.50.

BSS8. Interrelations Between Cement and Concrete Properties : Part 3, Compressive Strength of Mortars. 55 cents. BSS9. Thermal-Shock Resistance for Built-up Membranes. 20 cents. BSSIO. Field Burnout Tests of Apartment Dwelling Units. 25 cents. BSSll. Fire Resistance of Steel Deck Floor Assemblies. 25 cents. BSS12. Performance of Square-Edged Orifices and Orifice-Target Combinations as Air Mixers. 15 cents. BSS13. Shrinkage and Creep in Prestressed Concrete. 15 cents. BSS14. Experimental Determination of Eccentricity of Floor Loads Applied to a Bearing Wall. 15 cents.

Send orders with remittance to: Superintendent of Documents, U.S. Government

Printing Office, Washington, D.C. 20402. Remittances from foreign countries should include an additional one-fourth of the purchase price for postage.

[See mailing list announcement on last page.]
UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Interrelations Between Cement and

Concrete Properties, Part 4

Shrinkage of Neat Portland Cement

Pastes and Concretes

R. L. Blaine, H. T. Arni, and D. N. Evans

Building Research Division

Institute for Applied Technology

National Bureau of Standards Washington, D.C. 20234

Building Science Series 15

Issued March 1969

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C, 20402 - Price 75 cents
NATiaWAL BUREAU OF STANDARD?

Contents

Page Section 9. Shrinkage of hardened portland cement pastes 1 R. L. Blaine, H. T. Arni and D. N. Evans,

Section 10. Shrinkage and Expansion of Concrete 37

R. L. Blaine and H. T. Arni

Library of Congress Catalog Card Number: 64-60095
Section 9. Shrinkage of Hardened Portland Cement Pastes

R. L. Blaine, H. T. Arni, and D. N. Evans

The relationship between cement properties and drying shrinkage of partially hydrated neat cement pastes of normal consistency made of a large number of portland cements of different types and composition were studied by fitting multivariable regression equations with the aid of a digital computer. The time of cracking of annular speci- mens restrained from shrinking by a steel core varied from 0.1 to more than 40 hours. The principal variables which appeared to have the greatest effect were the fineness and

K2O and C4AF contents of the cements. The fineness and K2O contents of the cements appeared to have the greatest effect on the nonrestrained shrinkage of prisms at the time of cracking of the annular specimens. The shrinkage of neat cement bars after 1, 6, 27 days, and 6 months in laboratory air differed greatly with different cements. The principal variables appeared to be the C3A, SO3, and C3A/SO3 ratios. Other commonly

determined variables were associated with each of the above test values. The trace ele- ments, other than Na20 and K2O, were not generally associated with the shrinkage or cracking characteristics. Keywords: Chemical composition of portland cements; cracking of portland ce- ments; cracking resistance of cements; portland cement; shrinkage

of Portland cements; trace elements.

Page

1. Introduction 1

2. Materials 2

3. Tests and nomenclature 2

4. Statistical treatment 4

5. Results of tests 4

5.1. Nonrestrained shrinkage after 24 hr drying 4

5.2. Nonrestrained shrinkage after 6 days drying 8

5.3. Nonrestrained shrinkage after 28 days drying 9

5.4. Nonrestrained shrinkage after 6 months drying 11

5.5. Time of cracking of annular specimens re- strained from shrinkage 14

5.6. Nonrestrained shrinkage of prisms at time of cracking of annular specimens 19

5.7. Ratio of nonrestrained shrinkage at time of cracking of annular specimens to the nonrestrained shrinkage at 7 days, (SB/S7).. 21

Page

5.8. Ratio of nonrestrained shrinkage of bars at time of cracking of the annular specimens

to the nonrestrained shrinkage of the bars

at 28 days, (SHBR/SH28) or (SB/S28).- 23

5.9. Results of duplicate determinations 27

5.10. Comparative test-values on other hydraulic cements 27

5.11. Comparison with cements from other sources

6. Discussion 28

6.1. Nonrestrained shrinkage versus age 28

6.2. Trends of variables 28

6.3. Shrinkage characteristics of neat cement

pastes versus compressive strength of

1: 2.75 (cement to sand) mortars 31

7. Summary and conclusions 33

8. References 35

1. Introduction

Many hundreds of articles have been published relative to the drying shrinkage of portland cements, mortars, and concretes. Many of

these have been reviewed, discussed, and referenced in the various international symposia on

the chemistry of cements,—in Stockholm, in

1938 in London in 1952 [2], and in Washington in 1960 [3]. These many articles attest, to some extent, to both the importance and complexity of the phenomenon.

These reports of investigations of the many

variables associated with drying shrinkage in-

^ Figures in brackets refer to literature references at the conclusion of this section, p. 35.

eluded information on the effects of fineness,

tri-calcium aluminate, gypsum, and the alkalies

in the cements. Little or no information was

presented on the effects of other differences in

the composition of the cements, or of possible

effects of trace elements on the drying shrinkage. The shrinkage was generally recognized to

result from the drying or changes in moisture

content of the colloidal material or gel formed

as the hydration product of the cement.

At the time the present study of the interrelation between cement and concrete properties was initiated, a test method had been proposed [4] for determining amount of shrink1
age of the nonrestrained bars and the time of

cracking of annular specimens of partially hydrated neat cement pastes. This test method

appeared, at that time, to offer a means for

evaluating shrinkage and cracking characteristics of the different cements. Shrinkage tests were, however, also made on concrete specimens, as information was required on the degree of correlation of tests made on the neat

pastes and those made on the concretes. This section of this series of articles deals

primarily with the variables associated with

the shrinkage characteristics of the neat ce- ment pastes. The studies of shrinkage of concretes made from these cements will be presented in the following section.

2. Materials

The Portland cements used in this study have

previously been described [5, 6, 7] . Briefly, they

consisted of 199 commercially manufactured

Portland cements of the different types, and

obtained from different areas of the USA, with

a few obtained from other countries. These were classified primarily on the basis of their

chemical composition and physical tests, and

included 82 Type I, 68 Type II, 20 Type III, 3 Type IV, and 12 Type V cements. Also included were 14 air-entraining cements. The

chemical analyses and other tests previously re- ported in previous sections of this series of

articles [6, 7, 8, 9, 10, 11, 12] indicated that the

cements had a fairly broad range of compositions and properties.

3. Tests and Nomenclature

Neat Portland cement pastes were mixed

using a mechanical mixer specified for mixing

hydraulic cement mortars [13]. The percentage

mixing water used with 1000 g of cement was

the same as that previously required [6] for

normal consistency of each of the cement samples. The mixing time was the same as that

required for hand mixing. The first 30 s were

at the No. 1 speed and next 60 s at the No. 2

speed [13]. A determination was then made of

the Vicat penetration. This paste was then re- turned to the mixing bowl and the whole mass

remixed for 15 s before filling the molds. Two

types of molds were used,—one for 1 X 1 X

10-in (effective-gage-length) specimens for

nonrestrained shrinkage ^ measurements, and

the second for annular specimens for determining the time of cracking of specimens restrained

from shrinkage by a chromium-plated steel disc 1 in thick and 3.25 in in diameter, see

figure 9-1 ^. The cement paste was tamped into the lightly

greased molds, troweled flush with the tops of

the molds, covered with plastic, and then cured

at 73 ± 1 °F and 95 to 100 percent relative

humidity for 24 hours. The specimens were

then removed from the molds and exposed to air in the laboratory at 73 °F and 50 ± 5-percent relative humidity. The length of each

prism was measured when removed from the

mold and a line of conducting paint was placed near the outer edge on each annular specimen.

'The term "nonrestrained" or "free" shrinkage as used in this

article indicates that no external restraint or force was used. It does not imply that the intrinsic internal restraints dependent on

the size and shape of the specimens, the amount of nonhydrated cement in the paste, and the rate of evaporation of water from

the specimens do not exist.

^ The mold dimensions and test procedures were modified from

those proposed in the RILEM specification to permit use of avail- able prism molds. The cross sectional areas and the areas of the

surfaces exposed to the laboratory air were approximately the same

for the bars and annular specimens.

ASSEMBLY VIEW

Figure 9-1. Mold for use in making annular

specimens.

The removable brass ring (1) and base plate (2) held the chrome plated steel disc (3) in place with the center (4) during placing and tamping

of the neat cement paste in the annular space. Up to six pairs of prisms and annular specimens were supported in a rack (see figure 9-2)

and arranged so that the length changes of the

prisms could be measured continuously by means of the dial gages which were graduated

to 0.0001 in. The electronic detecting device

(see figure 9-3) was used to turn off an electric

clock when an annular specimen with a steel core broke because of drying shrinkage.

2
Figure 9-2. Rack for supporting bars and annular speci- mens for non-restrained and restrained shrinkage tests.

The length changes of the prisms or bars were measured at 15 and 30 min, 1, 3, 6, and 24

hr after removal from the molds or when it was noted that one of the clocks had stopped.

An automatic camera was used to photograph

the equipment with the dial gages and clocks

every hour after the regular work day. The

length measurements of the prisms at the time

of breaking of the annular specimens were interpolated from the readings or from the pictorial records. At 24 or 48 hr after removal

from moist-air storage (depending on the

time of cracking of the annular specimen) the

prisms were removed from the rack, measured

with a standard comparator, and then placed on another rack in the laboratory at 73 °F and

50-percent relative humidity, and length measurements made at 7 and 28 days, 6 months, and

1 year.

The rack holding the specimens after they were first removed from the molds and moist

storage was maintained in one position in the

laboratory for the duration of tests on all the

specimens. The rate of air-flow and humidity

may have varied to some extent during the

months required to make the tests. No attempt

+ lOOV

Figure 9-3. Diagram of electrical circuit used for stopping the electric clocks at time of cracking of the annular specimens.

With a specimen of low electrical resistance in place between terminals A & B, there

is a drop of 20 V across the two parallel resistors of 600 Q and 500K. The potentiometer (c) can then be adjusted to apply any desired grid bias from 0 to —20 Volts, thus controlliner the plate current through the 6L6 tube. This is set at a point so as

to just keep the relay closed. Upon breaking of the sample the resistance between

points A & B increases. This causes point B to become more negative with respect to point A, which in turn increases the negative bias applied to the grid of the 6L6,

resulting in a decrease of current through the tube, opening the relay, and stopping

the clock.

' was made to control the CO2 content of the air

surrounding the specimens. However, there is

Ji no reason to believe that it varied greatly from

|i day to day.

With the large amount of data collected it was necessary to limit that which could be presented in this section. The notations or abbreviations used to designate the variables measured

are as follows

SH24, percentage shrinkage of prisms at 24

hr

;

SH07, percentage shrinkage of prisms at 7

days;

SH28, percentage shrinkage of prisms at 28

days;

SH6M, percentage shrinkage of prisms at 6

months

;

3
TOBR, time in hours for annular specimen to crack

;

SHBR, percentage shrinkage of the prisms at the time of cracking of the annular

specimen

;

SB/S7, = SHBR/SH07 (see above) ; SB/S28, = SHBR/SH28 (see above).

Other notations and abbreviations are the

same as those used in previous sections in this

series of articles

Duplicate tests were made on different days

using 20 Portland cements obtained separately

in order to evaluate the reproducibility of val- ues for the nonrestrained shrinkage of the

prisms and time of cracking of annular speci- mens.

4. Statistical Treatment

The statistical treatment of the shrinkage

data was the same as that used in previous sec- tions of this series of articles and it was described in detail in part 1, section 1 [5]. Briefly,

these techniques included preliminary plots of

the dependent versus major independent variables. After it had been determined which of

the independent variables appeared significantly related to the dependent variable when

used in a multivariable regression equation,

the residuals of the equation were fitted by a

least squares method to other single independent variables and the reduction in variance

calculated. If any of the additional independent

variables indicated a significant reduction in

variance, they were tried in the multivariable

equation and retained if the coef./s.d. ratio was greater than 1 ^.

As in previous sections, equations were cal- culated using both the potential compounds and

the oxides as principal independent variables,

then with commonly determined independent

variables, and then with the trace elements as added independent variables. This was done

both with AE + NAE cements and with NAE

cements alone. The significance of reduction in

the S.D. values resulting from the use of the

additional variables was calculated from vari- ous pairs of equations. Equations were also

calculated for the "odds" and "evens" in the

array of cements.

A large number of trial equations were cal- culated in order to ascertain that values of all available independent variables were considered.

5. Results of Tests

5.1. Nonrestrained Shrinkage After 24 Hr.

Drying

The results of preliminary plots of the nonrestrained shrinkage of the neat cement prisms

at various ages versus individual independent

variables are presented in figure 9-4. The lines

drawn through the 12 pairs of averages to indi- cate the trend, and the significance of the number of points in the opposite quadrants as well as the "quadrant sum" have previously been

discussed in section 1, subsections 4.1 and

5 [5]. It may be noted that for the 24-hr shrinkage (SH24), SiOa AI2O3, FeaOs, SO3, K2O, total

alkali, C3A, C2S, C4AF, fineness, and air, 1 : 4

mortars) all had "quadrant-sum" absolute val-

* Included among those notations etc. are the use of C3A, C3S,

CzS, and C4AF for the calculated potential compound composition

of the cements, viz, tricalcium aluminate, tricalcium silicate, dieal- cium silicate and tetraealcium aluminoferrite. Also used are Loss

for loss on ignition, Insol for insoluble residue, and APF for air- permeability fineness. Also used are AE + NAE to designate air- entraining plus non-air-entraining cements and NAE for the nonair-entraining cements. The compressive strength in psi of 1:2.75 (cement to sand) mortars cured for 1, 3, 7, 28 days, and 1 year

are designated by STOl, ST03, ST07, ST28, and STIY respectively.

^ The statistical terms used in this section are the same as those used in previous sections. For example, S.D. refers to the estimated standard deviation calculated from the residuals of a fitted equation, or the estimated standard deviation about an average. Also, as in previous sections, s.d. refers to the estimated standard deviation of the coefficient of an independent variable used in a fitted equation;

coef./s.d., the ratio of the estimated coefficient (of an independent

variable used in an equation) to its estimated standard deviation; and "F" = Fisher's ratio of variances. As indicated in previous

sections a coef./s.d. ratio greater than one was considered to be of

sufficient significance to warrant further investigation. D.F. is used

to designate the number of degrees of freedom.

ues equal to or greater than 11, a value which

may be considered significant at the 5-percent

probability level. Multivariable regression equations are considered of the greatest significance

in evaluating the association of the different

independent variables to the dependent variable. Some of the limitations on interpretation

of multivariable regression equations, as well

as other statistical techniques used in this series

of articles, have been discussed in section 1, subsections 4.2, 4.3, and 5. [5].

The frequency distribution of the 24-hr percentage-shrinkage values are presented in

table 9-1. Each of the types of cement, as

classified,*^ had a considerable range of shrinkage values, and there was considerable over- lapping of the values obtained with the different types.

Selected equations relating the percentageshrinkage values of the AE + NAE cements at 24 hr to various independent variables are presented in table 9-2. Equation 1 presents the

relationship for shrinkage to Wi, the percentage water required for normal consistency of

* As previously indicated [6], the cements were classified primarily on the basis of the chemical analysis and physical tests such as air- entrainment, fineness, etc.

' The equations selected were primarily those which indicated the

association with dependent variables of commonly determined vari- ables having coef./s.d. ratios greater than 1 when used in multi- variable equations, and also indicated which of minor and trace elements might also have had an effect. 4
SHRINKAGE

TIME NOTE

INDEPENDENT VARIABLES

Si O2 AI2O3 FegOj CaO MgO SO3 NogO K2O TOTAL

ALKALI C3A C3S CgS C4AF AF _S_ A+F

AIR.R

FINE WAGN,

FINE AIR

1:4 MOR

24 HOURS

(1)

(2)

(3)

(4) NL

-15

84 V

+ 11

8

, 4VIV.

NL

-12

6

6

NO

-2

8

4 \/

L? +6

102

1 J

NL

+ 18

84 v

+ 3

12

NL +24

10

NL + 1!

10

L=Z

NL + 14

10

L? + 9

10

iC

NL

-15

10

NL

-16

84

1 ; LL.

NL

+13

6

1 NO-6

10 V

+ 13

102 v

L? + 11

10 |>

L? + 17

1

6 DAYS

(1)

(2)

13) (4)

10

NL

-14

12 \yV

L +24

10 K1 \

L? -8

10 ^31 V.

NL

-10

10 |>v

L? +8

10

NL + 16

8 |>V

L?

+10

12

LZ.

NL

+24

10

NL

+16

10 0NL +146

1 6

NO

+ 1

10 K1 \

L?^7

10

1 \

L? -16

10 V

L? +9

8 K1 \

L?-5

10 |>V

L?+8

e |>|/

10 |>

L? + 17

27 DAYS

(1)

(2)

(3)

(4)

10

1 V

NL

-15

10 V

L?

+12

8 K1 \

L?

-7

8 K1 \

u?-8

8 v

L?+6

10 \yV

L?

+15

8 v

L?+9

12

NL

+24

10 \^

NL

+17

10 \^

NL +14

6

1

^

NO+4

12

NL

-24

9 K1 \

L?

-13

10 \yV

L? + 18

10

1 \

L? -10

6

1

^

NO + 3

8

1 4

NO

0

10

L?

+ 13

6 MONTHS

(1)

(2)

(3) (4)

12 |\

NO

-24

10 l>V

L?+7

8 K1 x

L?

-lb

6

1 NO-7

8 |>V

L?

+12

8

vLL? + 12

8

L? +7

10 1^V

L +20

10 l>V

L + 17

10 1^V

L? +9

8

1 4

NO

-3

12 1^1 \

L? -24

8 Ki \

L? -6

10 \yV

L? +14

8 Ki \

L? -9

6

1

^

NO + 2

8

1 4

NO-2

10 l>

L? + 12

Figure 9-4. Results of plotting on the "Y" axis the percentage shrinkage in laboratory air at 2U hours, 6 days, 27

days, and 6 months of neat portland cement pastes of normal consistency cured for 2U hours in moist air versus

various independent variables on the "X" axis.

* Note (1) Ratio of number of plotted points in pairs of diametrically opposite quadrants. Note (2) General trend of lines drawn through plotted points. Note (3) Apparent nature of relationship. L = linear; NL =: nonlinear; NO = no apparent relationship; and L? = nature of rela- tionship not determinable. (Note (4) Quadrant sum in corner test (see reference 5).

Table 9-1. Frequency distribution of cements with respect to percentage shrinkage of neat cement pastes of normal consistency after 24

hr drying in laboratory air following 24 hr moist-air curing (SH24)

Percentage shrinkage

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 Type cement to to to to to to to to to to to to and Total

0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 over

Number of cements

I 5 22

1 17

22

2

19

8

19

2

4

10

3

1

1 2 1 3 1 1 1 778

60

2

192

14

lA

11 13 1 1 IIA

III 1 7 1

1 4 1 1 IIIA 1 IV, V 1 3 6 2 2

Total 1 21 47 52 26 15 6 4 2 4 2 1 1 182

the neat pastes. The estimated S.D. value obtained in eq 1 was lower than the estimated

S.D. of the cements about their average (note

1 of table 9-2). By reference to table 9-34 « it may be noted that the relationship was significant at the 1-percent probability level. Equation 2 of table 9-2 presents the relationships for some commonly determined variables

plus the C3A/SO3 ratio. The use of Q^A, SO^,

and CaA/SO:^ as independent variables was

found in preliminary trial equations to result

* A tabulation of the reduction in variance or "F" values for all equations compared is presented in table 9-34, page 27. Presented also are the critical values for "F" which, if equalled or exceeded, indicate

significance at the 1-percent and 5-percent levels for the number of degrees of freedom (D.F.) involved in each comparison.

in lower S.D. values than when the C3A/SO3

ratio was not used. The variables APF, Ba, P,

Zn, and Cr had coef./s.d. ratios greater than 1 when included with the variables in eq 2 (eq 3)

,

and the reduction in variance was significant at the 1-percent probability level (table 9-34). Of

these added variables, however, only APF and

Cr had coef./s.d. ratios greater than 2. Equations 3A and 3B, calculated with the

"odds" and "evens" in the array of cements,

had coef./s.d. ratios less than one for the "odds"

or "evens" or both, for C^A, APF, Ba, P, and

Zn. As indicated in previous sections, this may

occur when (1) the coef./s.d. ratio is not significant in the equation for all the values, or

5
Table 9-2. Coefficients for equations relating the percentage shrinkage at 24 hr (after the NAE cements to various in

Equation

1..

2..

3..

3A.

3B.

4..

5..

5A.

SB.

Note Const. CsA C4AF AI2O3 Fe203

SH24 0.01241

s.d. = (0.01734) SH24 =-0.00317

s.d. = (0.01558) SH24 =-0.01903

s.d. = (0.01579) SH24 (odd) =-0.01123

s.d. = (0.02211) SH24 (even) = -0.02046

s.d. = (0.02466) SH24 =-0.02801

s.d. = (0.01859) SH24 0.03981

s.d. = (0.01855) SH24 (odd) 0.02792

s.d. = (0.02441) SH24 (even) =-0.05720

s.d. = (0.03540)

-0.00514

(0.00173) -0.00464

(0.00171) — 0.00608

(0.00228)

* — 0.00273

(0.00290)

-0.001457

(0.000465) -0.001307

(0.000455) — 0.001979

(0.000735) — 0 . 000837

(0.000594) -0.01094

(0.00375) -0.01217

(0.00371) -0.01425

(0.00465) -0.01215

(0.00761)

-0.00431

(0.00114) -0.00450

(0.00112) -0.00559

(0.00183) -0.00403

(0.00147)

» 163 cements; Avg = 0.0643; S.D. = 0.01427. ^ 82 cements. ' 81 cements. * Coef./s.d. ratio less than 1.

Table 9-3. Coefficients for equations relating the -percentage shrinkage at 24 hr {after the cements, to various inde

Equation Note Const. CaA C4AF AhOs Fe203 NazO

3A3B.

5A.

5B.

SH24

s.d. SH24

s.d. SH24

s.d.

0.00196 = (0.01738) 0.00182 = (0.01557) = -0.01970 = (0.01581) SH24 (odd) = -0.01592

s.d. = (0.02145) SH24 (even) =-0.01472

s.d. = (0.02538)

-0.005779

(0.001744) -0.005532

(0.001715) -0.005957

(0.002247) -0.004410

(0.002904)

-0.001531

(0.000466) -0.001367

(0.000451) -0.001455

(0.000643) -0.001007

(0.000706) SH24

s.d. SH24

s.d.

-0.01726

' (0.01874) = -0.03589 = (0.01856) SH24 (odd) =-0.02438

s.d. = (0.02426) SH24 (even) = -0.06950

s.d. = (0.03376)

-0.01292

(0.00370) -0.01328

(0.00367) -0.01290

(0.00475) -0.01852

(0.00683)

-0.00455

(0.00116) -0.00461

(0.00111) -0.00431

(0.00161) -0.00429

(0.00167)

+0.00733

(0.00546) +0.01004

(0.00531) *+0. 00304

(0.00945) +0.00982

(0.00633) +0.00593

(0.00534) +0.00874

(0.00516) *+0. 00112

(0.00938) +0.00907

(0.00597)

» 151 cements; Avg = 0.06328; S.D. = 0.01366. 2 76 cements. 3 75 cements. * Coef./s.d. ratio less than 1. (2) when a preponderance of the cements with

very high or very low values for an independent

variable happens to fall within one of the

groups. Zn and P are particularly vulnerable to the second of the above contingencies because

of the comparatively small number of cements

for which nonzero values for these two elements were reported.

Equations 4 and 5 of table 9-2 were calculated using the oxides instead of the calculated

potential compounds. The use of the trace ele- ments in eq 5 in addition to the commonly determined variables in eq 4 resulted in a reduction in variance significant at the 5-percent

probability level (see table 9-34). Again, only APF and Cr. had coef./s.d. ratios greater than

2. In eqs 5A and 5B which were calculated for

the "odds" and "evens", APF, Ba, Zn, and P

had coef./s.d. ratios less than 1 in one or the

other of the equations.

A comparable series of equations is presented

in table 9-3 for NAE cements. The coefficients

of the independent variables are in reasonable

agreement with those in table 9-2. Rb had a

coef./s.d. greater than 1 in eq 5, and in the

equations for the "odds" and "evens", (eqs 3A,

3B, 5A, and 5B) NasO, Ba, and P had coef./s.d.

ratios less than 1 in one or the other of the

smaller groups. The sign of the coefficient for

Zn was positive in eqs 3A and 5A and negative

in eqs 3, 3B, 5 and 5B. In none of these in- stances were the coefficients highly significant.

Using the independent variables and their

coefficients from eq 3 of table 9-3, and the

6
initial 24- hr moist-air storage) oJ neat-cement bars of normal consistency made of AE +

dependent variables (SH24)

K2O SO3

+0.01729

(0.00428) +0.02006

(0.00448) +0.03013

(0.00696) +0.01141

(0.00599) +0.01917

(0.00440) +0.01963

(0.00442) +0.02922

(0.00686) +0.01143

(0.00590)

+0.03889

(0.00760) +0.03665

(0.00799) +0.03574

(0.01083) +0.03272

(0.01348) +0.04310

(0.01014) +0.04603

(0.00993) +0.04520

(0.01243) +0.05558

(0.02083)

C3A/SO3

+0.00925

(0.00310) +0.00876

(0.00304) +0.01037

(0.00407) +0.00622

(0.00515)

AI2O3/SO3

+0.02078

(0.00656) + 0.02288

(0.0064.3) +0.02389

(0.00801) +0.02517

(0.01340)

APF

+0.0000047

(0.0000020) *+0.0000030

(0.0000033) +0.0000047

(0.0000026) +0.0000035

(0.0000020) +0.0000042

(0.0000020) *+0. 0000030

(0.00000.33) +0.0000036

(0.0000027)

Ba

+0.04551

(0.03263) +0.05713

(0.04112) 0.06883

(0.09156)

+ 0.05175

(0.03228) + 0.06262

(0.04071) 0.07342

(0.08952)

+0.01079

(0.00815) +0.02026

(0.01138) -0.00861

(0.01204)

+0.01122

(0.00806) +0.02134

(0.01125) "-0.00845

(0.01185)

Zn

-0.0346

(0.0306) -0.0027

(0.0451) *-0.0435

(0.0445)

-0.0390

(0.0302) *-0.0101

(0.0444) -0.0552

(0.0447)

Cr

+0.4462

(0.2059) +0.5257

(0.3129) +0.4258

(0.2787)

+0.4531

(0.2033) +0.5561

(0.3079) +0.4378

(0.2745)

+0.00310

(0.00070)

initial 24 hr moist-air storage) of neat-cement bars of normal consistency made of NAE

pendent variables {SH24)

K20 SO3 C3A/SO3 AI2O3/SO3 APF Ba P Zn Cr Rb W 1 S.D

+0.00264

(0.00070) 0.01310

+0.01730

(0.00436) +0.02004

(0.00452) +0.02536

(0.00683) +0.01482

(0.00605) +0.01655

(0.00431) +0.01604

(0.00486) + 0.02.377 (0.00751) + 0.00966

(0.00619)

+0.03907

(0.00764) +0.03506

(0.00791) +0.03388

(0.01024) +0.03301

(0.01394) +0.04762

(0.00955) +0.04577

(0.00979) +0.04012

(0.01232) +0.06589

(0.01928)

+0.01020

(0.00310) + 0.01012

(0.00302) + 0.01031

(0.00396) + 0.00381

(0.00506)

0.01064

+ 0.0000046

(0.0000020) + 0.0000045

(0.0000032) + 0.0000041

(0.0000028)

+0.052.33 (0.03194) +0.06645

(0.03715) *- 0.08642

(0.08693)

+0.01302

(0.00803) +0.02752

(0.01119) *-0. 00841

(0.01192)

-0.03234

(0.02979) +0.06508

(0.06129) -0.05719

(0.03401)

+0.4422

(0.2074) +0.5193

(0.2870) +0.3252

(0.3087)

0.01020

0.01058

0.00960

+0.02272

(0.00649) +0.02400

(0.006.32) +0.02158

(0.00807) +0.03545

(0.01195)

0.01062

+ 0.0000044

(0.0000020) + 0.0000045

(0.00000.33) +0.0000030

(0.0000027)

+0.06093

(0.03154) +0.07151

(0.03736) *- 0.07405

(0.08275)

+0.01148

(0.00801) +0.02648

(0.01171) *- 0.00734

(0.01136)

-0.03266

(0.02947) +0.06876

(0.06146) -0.06432

(0.03289)

+0.3713

(0.2099) +0.4604

(0.3082) +0.3388

(0.2960)

+0.8259

(0.5065) *+0.4243

(0.8129) +0.9599

(0.6391)

0.01004

0.01060

0.00915

ranges of these variables, values were calculated for their contributions and ranges of their

contributions to the 24-hr percentage-shrinkage values. These calculated values, as presented in table 9-4, are estimates based on a

single equation, and it may be noted that some- what different values would be obtained by use

of other equations ^. As in previous sections, the calculated-contribution values must also take into consideration the constant in the equation.

An increase in C3A and C4AF appears to be

associated with lower shrinkage values but the

use also of the SO.j and the C3A/SO3 ratio in

the equation may have affected the coefficient

° Similar computations for contributions to the shrinkage values

at other ages will also be made from corresponding equations in order that the trends may be followed more easily.

Table 9-4. Calculated contributions of independent variables to the percentage shrinkage at 24 hr. {after the initial 24 hr. in

moist-air storage) of neat-cement bars of normal consistency

(SH24)

Calculat- Inde- Ranges of Coefficients Calculated contri- ed ranges pendent variables, from eq 3 butions to SH24 of contri- variable percent table 9-3 butions to SH24

Const. = -0.020 CsA 0 to 15 -0.00553 0 to -0.083 0.083 C4AF 4 to 17 -0.00137 -0.005 to -0.023 0.018 Na20**.,. 0 to 0.75 +0.0100 0 to +0.008 0.008 K2O 0 to 1.1 +0.0200 0 to +0.022 0.022 SO3 1.2 to 3.6 +0.0351 +0.042 to +0.126 0.084 C..A/SO3-- 0.4 to 10.1 + 0.0101 +0.004 to +0.102 0.098 APF *2500 to 5500 +0.0000046 +0.012 to +0.025 0.013 Ba** 0 to 0.2 +0.0523 0 to +0.010 0.010 p*+ 0 to 0.5 +0.0130 0 to +0.006 0.006 Zn** 0 to 0.2 -0.0323 0 to -0.006 0.006 Cr 0 to 0.02 + 0.442 0 to +0.009 0.009

*craVg.

**Coefiicient of doubtful significance as coef ./s.d. ratio was less than 2.

7
for the C3A. Differences in the C.^A and SOs

appear to be important contributors to differ- ences in shrinkage.

5.2. Nonrestrained Shrinkage After 6 Days

Drying

It may be noted in figure 9-4 that Si02, AI2O3,

SO3, K2O, total alkali, C3A, and (air, 1 : 4 mortar) all had absolute "quadrant-sum" values

greater than 11 when the shrinkage at 7 days

(the first 24 hr in moist storage) was plotted versus the individual independent variables.

The frequency distributions of the 7-day percentage-shrinkage values of the neat pastes of

normal consistency of the different types of

cement are presented in table 9-5. There was a

considerable range of values, especially for the

Type I cements, and an overlapping of the val- ues for the cements within the various types as

classified.

Equations selected from those computed to determine the various independent variables as- sociated with the shrinkage at 7 days (the first 24 hr in moist-air storage) of neat cement bars

of normal consistency made of AE + NAE ce- ments, are presented in table 9-6. Equation 1

relates the shrinkage to the percentage water

used for normal consistency of the neat pastes.

The coef./s.d. ratio for the Wi was less than 2,

and the reduction in variance was not significant at the 5-percent probability level (table

9-34).

Table 9-5. Frequency distribution of cements with respect to percentage shrinkage of neat cements of normal consistency after 6 days

drying in laboratory air after 24 hr moist-air storage {SH07)

Type cement

Percentage shrinkage

Total

0.080

to 0.100

0.100

to 0.120

0.120

to 0.140

0.140

to 0.160

0.160

to 0.180

0.180

to 0.200

0.200

to 0.220

0.220

to 0.240

0.240

to 0.260

0.260

to 0.280

0.280

to 0.300

0.300 and

over

Number of cements

I 2 7 20

1 15

22

214

19

113

9

13

1

1

6 1

1

1

2

1

1

1 2 3 778

60

2

192

14

lA

II 1 15 4 IIA

III 1 2 2

1

1 1 IIIA

IV, V 1 3 5 4

Total 4 26 43 52 29 13 4 5 1 2 3 182

Table 9-6. Coefficients for equations relating the percentage shrinkage at 7 days (the first cements, to various inde

Equation Note Const. CsA CiAF AI2O3 FezOs CaO

1 SHOT =+0.0803

s.d. = (0.0356) SH07 =+0.1147

s.d. = (0.0176) SH07 =-0.0118

s.d. = (0.0353) SH07 =-0.0225

s.d. = (0.0344) SH07 (odd) =-0.0143

s.d. = (0.0421) SH07 (even) = -0.0405

s.d. = (0.0704) SH07 =+0.4203

s.d. = (0.1291) SH07 =+0.1362

s.d. = (0.1317) SH07 =+0.1890

s.d. = (0.1268) SH07 (odd) =+0.3419

s.d. = (0.2024) SH07 feven) =+0.0187

s.d. = (0.1772)

2 *- 0.00010

(0.00086) -0.01389

(0.00383) -0.01423

(0.00371) -0.01266

(0.00465) -0.01702

(0.00745)

-0.001344

(0.001108) -0.001382

(0.001038) -0.001525

(0.001007) -0.002051

(0.001409) *- 0.001282

(0.001626)

3 .

4

4A

4B

5 *-0. 00111

(0.00273) -0.03343

(0.00848) -0.03553

(0.00814) -0.03072

(0.01053) -0.06140

(0.01645)

-0.006786

(0.003052) -0.005471

(0.002918) -0.006824

(0.002822) -0.010100

(0.004255) -0.005482

(0.004054)

-0.004490

(0.001878) -0.002810

(0.001966) -0.003900

(0.001904) -0.005834

(0.003107) -0.003327

(0552.002)

6

7

7A

7B

» 165 cements; Avg = 0.1481; S.D. = 0.02813. 2 83 cements. = 82 cements. * Coef./s.d. ratio less than 1.

8
Only C3A, C4AF, and SO3 were used as independent variables in eq 2. The coef./s.d. ratio

for C3A was less than 1. It may be noted that in

eq 3, where C3A/SO3 and four other additional

independent variables were used, the coefficient

for C3A was highly significant, and that the

1 coefficient for SO3 more than doubled. The reI duction in the S.D. value was highly significant

j (see table 9-34) . Coef./s.d. ratios for C4AF and

I APF, however, were less than two. By use of

j the trace elements, Ba, P, and Rb in eqs 4 and

i 7, a further significant reduction in the S.D.

J was attained, although P had a coef./s.d. ratio

I less than 2. In the equations for the "odds" and

"evens" (eqs 4A and 4B), P and Rb had coef./

s.d. values less than one in one or the other, as may also be noted in eqs 7A and 7B, where the

oxides were used instead of the calculated compounds. Equations 5, 6, and 7, calculated using

the oxides, also indicate that the coefficients for

AI2O3 and SO3 are affected by inclusion of the

AI2O3/SO3 ratio.

A comparable series of equations for the

NAE cements is presented in table 9-7. The coefficients obtained were fairly similar to those

, of the previous table except that the coefficient

I for (air, 1 : 4 mortar) was of questionable

significance when the AE cements were not included. The coef./s.d. ratio for (air, 1: 4 mortar) was less than 1 in eqs 4A and 4B in table

9-7. It was also less than one when this variable was included with those in eq 7. Of the minor

constituents, only P had coef./s.d. ratios of less than 1 in the equations for the "odds" or

"evens" and Rb had a coef./s.d. ratio greater

than 1 in all instances.

Using the coefficients of eq 4 of table 9-7

and the ranges of the independent variables,

values were calculated for their contributions

and ranges of contributions to the percentage

shrinkage at 7 days. These calculated values

are presented in table 9-8. Increases in C3A

and C4AF were associated with lower shrinkage values when SO3 and C3A/SO3 were included as independent variables. All the other

independent variables with coef./s.d. ratios

greater than 1 had positive coefficients. Variations of C3A, SO3 and C3A/SO3 appeared to have important effects. Although the coefficient

for (air, 1 : 4 mortar) was of doubtful signifi- cance when only the NAE cements were used in

the calculations, it was probably significant

when the AE cements were included as in

table 9-6.

5.3. Nonrestrained Shrinkage After 28 Days

Drying

The preliminary plots of the 28-day-shrinkage values (the first 24 hr in moist air) of the

neat cement pastes of normal consistency ver- sus various individual independent variables are indicated in figure 9-4. It may be noted that

SiOs, AI2O3, SO3, K2O, total alkali, C3A, C2S,

C4AF, A/F, and (air, 1 : 4 mortar) had "quadrant-sum" absolute values greater than 11. The frequency distribution of the 28-day

percentage-shrinkage values of the prisms

24 hr in moist-air-storage) of neat-cement bars of normal consistency made of AE-\-NAE

pendent variables (SHO?)

Na20 K2O SO3 C3A/SO3 AI2O3/SO3

Air, 1:4 mortar APF- Ba P Rb Wi S.D.

+0.00274

(0.00144) 0.02790 +0.02495

(0.00617) +0.06799

(0.01787) +0.06685

(0.01727) + 0.06063

(0.02147) +0.08050

(0.03558) + 0.02176

(0.00623) +0.09222

(0.02272) + 0.09462

(0.02173) +0.07894

(0.02678) +0.17189

(0.04657)

0.02659

+0.02825

(0.01249) +0.03017

(0.01215) +0.03384

(0.02147) +0.02890

(0.01590)

+0.04011

(0.01023) +0.03165

(0.01073) +0.03349

(0.01578) +0.02939

(0.01567)

+0.02410

(0.00689) + 0.02484

(0.00664) +0.02209

(0.00818 +0.02988

(0.01366)

+ 0.00143

(0.00055) +0.00171

(0.00054) +0.00139

(0.00082) + 0.00187

(0.00076)

+ 0.0000050

(0.0000045) +0.0000072

(0.0000044) +0.0000099

(0.0000069)

* +0.0000046

(0.0000064)

0.02404

+ 0.1675

(0.0698) +0.1601

(0.0808) + 0.1715

(0.1619)

+0.02401

(0.01662) + 0.04794

(0.02185) *-0. 01194

(0.02917)

+2.632

(1.115) *+ 1.292

(1.639) +3.336

(1.615)

0.02317

0.0236

0.02385

0.02622

+ 0.02225

(0.01229) +0.02409

(0.01185) +0.03060

(0.02109) + 0.02009

(0.01513)

+0.03300

(0.01080) +0.023.54 (0.01113) +0.02576

(0.01622) +0.01828

(0.01612)

+0.05723

(0.01499) +0.06167

(0.01439) +0.05163

(0.01798) +0.11148

(0.03020)

+ 0.00137

(0.00055) +0.00161

(0.00053) +0.00105

(0.00084) +0.00186

(0.00072)

+ 0.0000046

(0.0000045) +0.0000071

(0.0000044) +0.0000116

(0.0000068)

* +0. 0000014

(0.0000063)

0.02392 +0.2011

(0.0696) +0.2051

(0.0829) + 0.2016

(0.1527)

+0.02851

(0.01649) +0.05712

(0.02205) *+0. 01327

(0.02772)

+ 2.432

(0.099) *+ 0.989

(1.685) +3.223

(1..531)

0.02285

0.02347

0.02266

9
Table 9-7. Coefficients for equations relating the percentage shrinkage at 7 days (the cements, to various

Equation Note Const. CaA CiAF AI2O3 Fe203 CaO

SH07 =+0.0873

s.d. = (0.0361) SH07 =+0.1223

s.d. = (0.0180) SH07 =-0.0125

s.d. = (0.0350) SH07 =-0.0316

s.d. = (0.0346) SH07 (odd) =-0.0320

s.d. = (0.0467) SH07 (even) =+0.0358

s.d. = (0.0590) SH07 =+0.4202

s.d. = (0.1332) SH07 =+0.1503

s.d. = (0.1.342) SH07 =+0.2262

s.d. = (0.1271) SH07 (odd) =+0.1438

s.d. = (0.2030) SH07 (even) = +0.3954

s.d. = (0.1603)

*- 0.00047

(0.00087) -0.01666

(0.00383) -0.01649

(0.00372) -0.01754

(0.00520) -0.00715

(0.00625)

-0.001504

(0.001121) -0.001841

(0.001033) -0.001917

(0.001003) -0.001925

(0.001748) -0.002268

(0.001225)

3.

4

4A

4B

5 *- 0.00193

(0.00230^ -0.03578

(0.00849) -0.04005

(0.00801) -0.04181

(0.01065) -0.02224

(0.01544)

-0.006827

(0.003142) -0.006085

(0.002957) -0.008091

(0.002811) -0.007077

(0.004921) -0.010587

(0.003282)

-0.004370

(0.001935) -0.003113

(0.001988) -0.004495

(0.001899) -0.003232

(0.003054) -0.006087

(0.002271)

6

7.

7A

7B

» 153 cements; Avg = 0.1463; S.D. = 0.02748. 2 77 cements. ^ 75 cements. * Coef./s.d. ratio less than 1.

Table 9-8. Calculated contributions of independent variables to the percentage shrinkage at 7 days (the first S4 hr. in moist-airstorage) of neat-cement bars of normal consistency. (SH07)

Calculat- Inde- Ranges of Coefficients Calculated contri- ed ranges pendent variables, from eq 4 butions to SH07 of contri- variable percent table 9-7 butions to SH07

Const. = -0.032 CaA 0 to 15 -0.0165 0 to -0.248 0.248 C4AF**..- 4 to 17 -0.00192 -0.008 to -0.033 0.025 NaiO 0 to 0.75 +0.0313 0 to +0.023 0.023 K2O 0 to 1.1 +0.0383 0 to +0.042 0.042 SO3 1.2 to 3.6 +0.0722 +0.086 to +0.260 0.174 C3A/SO3-- 0.4 to 10.1 +0.0281 +0.011 to +0.284 0.273

Air, 1:4 mortar** 1 to 21 + 0.00144 + 0.001 to +0.030 0.029 APF *2500 to 5500 +0.0000088 + 0.012 to +0.048 0.026 Ba 0 to 0.2 +0.183 0 to +0.037 0.037 p** 0 to 0.5 +0.0262 0 to +0.013 0.013 Rb 0 to 0.01 + 2.667 0 to +0.027 0.027

*cmVg.

**Coefficient of doubtful signiiicance as coef./s.d. ratio was less than 2. made of the different cements is presented in

table 9-9. It may be noted that a considerable

range of values was obtained with each of the

different types of cement and especially with

those classified as Type I cements. The highest

percentage-shrinkage values were obtained

with the Type I or lA cements but some of the

Type I cements were also in the group with the

lowest percentage shrinkage.

A selected group of equations is presented in

table 9-10 to indicate the variables found to be

associated with the 28-day percentage-shrinkage values of the AE + NAE cements. Equation 1 indicates no apparent relationship between the percentage mixing water for normal

consistency and the percentage shrinkage at 28

days. The use of variables in eq 2 of this table,

resulted in a significant reduction in the S.D.

values (see table 9-34) although the C3A and

C4AF had coef./s.d. ratios less than 1. With the

use of the 5 additional variables in eq 3, the

variables C.3A, and C3A/SO.3 were highly significant, and C4AF had a coef./s.d. ratio greater

than 1. The additional use of the trace elements,

Ba, P, Zn, and Rb in eqs 4 and 6 resulted in a

reduction in variance significant at the 1-percent probability level. It may be noted that in

equations calculated for the "odds" and "evens"

in the array of cements (eqs 4A, 4B, 6A, and

6B) there were instances where C4AF, Si02,

FeaOa, MgO, APF, (air, 1:4 mortar), P, Zn,

and Rb had coef./s.d. ratios less than 1 in one

or more of the equations for the smaller groups.

A comparable series of equations for the

NAE cements is presented in table 9-11. In

these equations the (air, 1:4 mortar) had

coef./s.d. ratios less than 1 in trial equations

and was not included among the independent

variables. The coefficients for the other independent variables in table 9-11 appear to be

in reasonable agreement with corresponding

coefficients in table 9-10 where the AE cements were included.

Contributions and ranges of contributions to the shrinkage at 28 days of the neat cement

bars of normal consistency are presented in

table 9-12. The coefficients in eq 3 of table 9-11 were used as a basis for these calculations. The

three variables C3A, SO3, and C3A/SO3 when

used together in a multivariable equation had

the highest values for the calculated ranges of

10
first 24 kr in moist-air storage) of neat-cement bars vf normal consistency made of NAE

i independent variables

NasO K2O SO3 C3A/SO3 AI2O3/SO3

Air, 1:4 mortar APF Ba P Rb Wi S.D.

+0.00239

(0.00146) 0 . 02733

+0.02266

(0.00630) +0.08038

(0.01685) +0.07218

(0.01721) + 0.06717

(0.02410) + 0.04171

(0.02917) +0.01943

(0.00638) +0.09353

(0.02275) +0.10146

(0.02135) +0.09417 +0.06602

(0.043.59)

0.02633

+0.02475

(0.01322) +0.03133

(0.01274) +0.02664

(0.02410) +0.03270

(0.01411)

+0.04064

(0.01013) +0.03833

(0.01091) +0.04722

(0.01767) +0.02753

(0.01347)

+0.02814

(0.00686) + 0.02807

(0.00660) +0.02976

(0.00890) +0.01167

(0.01148)

+0.002116

(0.001253) +0.001444

(0.001217) *+0. 001141

(0.002186) *+0. 000685

(0.001.399)

0.02367

+0.0000088

(0.0000044) + 0.0000124

(0.0000079) +0.0000069

(0.0000054)

+ 0. 1828

(0.0684) +0.1053

(0.0867) +0.4800

(0. 14.37)

+ 0.02623

(0.01653) +0.04855

(0.02428)

* — 0.01348

(0.02373)

+ 2.667

(1.104) + 2.615

(1.786) + 1 . 795

(1.395)

0.02255

0 . 02483

0.01973

0.02598

+0.01907

(0.01309) +0.02928

(0.01149) +0.02383

tU.Uzlo4; +0.02927

(0.01224)

+0.03609

(0.01122) +0.03082

(0.01104) +0.04504

+0.01372

(0.01345)

+0.05995

(0.01490) + 0.06712

(0.01411) + 0.06910

\\J . \)\.<S\jO) +0.03899

(0.028.53)

+0.001950

(0.001249) +0.0000058(0.0000046) +0.0000090

(0.0000044) +0.0000125

\\j . UUUUU/ 0) +0.0000080

(0.00000.53)

0.02358

+ 0.2233

(0.0682) +0.1.391

(U . Uo/

Z

) +0.5488

(0.1373)

+0.03461

(0.01610) +0.0.59.39

*-0. 01109

(0.02259)

+ 2.511

(1.087) + 2.363

\l . i OZ) + 1.644

(1..326

0 . 02224

0.02444

0.01877

Table 9-9. Frequency distribution of cements with respect to percentage shrinkage of neat cements of normal consistency after 27 days

drying in laboratory air following 24 hr moist-air curing {SH28)

Percentage shrink age

0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 O..34 0.36 0.38 Type cement to to to to to to to to to to to to and Total

0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 over

Number of cements

I 2 5 11 143

14

17

17

17

6

16

12

10

15

4

13

1 2

1 2 3 77860

2192

14

182

lA

II 3 8 12 2 IIA

III 3 2

17

4

11

1 IIIA

IV, V 2 1 2 1

Total 7 14 28 41 34 16 22 9 2 1 3 2 3

contributions to the 28-day shrinkage-values.

Other independent variables, such as the alkalies and Ba, also appear associated with the

shrinkage values.

5.4. Nonrestrained Shrinkage After 6 Months

Drying

In the preliminary plots of the 6-months

shrinkage versus various individual independent variables it may be noted in figure 9-4

that SiOo, MgO, SO3, KoO, total alkali, CoS,

A/F, and (air, 1 : 4 mortar) had absolute

"quadrant-sum" values greater than 11. The frequency distributions of the different

types of cements with respect to the shrinkage

of neat cements of normal consistency after 6

months drying are presented in table 9-13. As

in the frequency-distribution tables at the

earlier ages (tables 9-1, 9-4 and 9-9) there was a spread of values of the cements within

each of the types, especially for the Type I cements, and an overlapping of the values obtained for the cements of the different types.

Equations selected from those computed to determine the various independent variables

associated with the 6-month-shrinkage values

of AE + NAE cements are presented in table

9-14. With the use of commonly determined

variables in eqs 1 or 3 there was a highly significant reduction in the S.D. values, (see table

9-34) and, with the additional trace elements,

11
Table 9-1 0. Coefficients for equations relating the percentage shrinkage at 28 days (the first cements, to various inde

Equation Note

(')

(')

(')

(1)

(')

(')

(')

(')

(')

(')

Const.

SH28

s.d. = +0

= (0 1935 0508) SH28

s.d. = +0

= (0 1297

0525) SH28

s.d. = +0

= (0 0119

0488) SH28

s.d. = -0

= (0 0129

0475) SH28 (odd)

s.d. = -0

= (0 0182

0577) SH28 (evpn)

s.d. = -0

= (0 0365

0976) SH28

s.d. = +0

= (0 2455

1387) SH28

s.d. = +0

= (0 1299

1627) SH28 (odd)

s.d. = +0

= (0 3095

2447) SH28 (even)

s.d. = -0

= (0 2049

2645)

C4AF

* — 0.00373 * - 0 . 00059

(0.00567) (0.00160) -0.01643 -0.001491

(0.00521) (0.001392) -0.01756 -0.001545

(0.00496) (0.001329) -0.01657 -0.00.3002

(0.00600) (0.001769) -0.02032 *- 0.000222

(0.01032) (0.000222)

Si02

-0.00751

(0.00409) -0.00.580

(0.00464) -0.01057

(0.00731) *- 0.00066

(0.00652)

AI2O3

-0.03898

(0.01108) -0.04133

(0.01108) -0.03685

(0.01372) -0.06752

(0.02260)

Ke20,i

-0.00822

(0.00354) -0.00779

(0.003.54) -0.01272

(0.00486) -0.00310

(0.00548)

MgO

+0.003261

(0.002317) +0.004797

(0.002292) +0.008882

(0.003351) *+0.002062

(0.003448)

+0.003964

(0.002477) +0.006216

(0.003616) 0.003007

(0.003676)

165 cements; Avg = 0.2247; S.D. =0.03976. 2 83 cements. ' 82 cements * Coef./s.d. ratio less than 1.

Table 9-11. Coefficients for equations relating the percentage shrinkage at 28 days (the cements, to various inde

Equation

1-.

2..

3..

3A.

3B

4..

5..

5A

5B

Note

(')

(')

(')

(') W

(•)

Const.

SH28

s.d. = +0

= (0 1256

0533) SH28

s.d. = +0

= (0 2251

0477) SH28

s.d. = -0= (0 0228

0466) SH28 (odd)

s.d. = -0

= (0 0192

0651) SH28 (even)

s.d. = +0

= (0 0492

0703) SH28

s.d. = +0

= (0 2616

1400) SH28

s.d. = +0= (0 1389

1601) SH28 (odd)

s.d. = +0

= (0 2407

2606) SH28 (even)

s.d. = +0= (0 2215

2154)

C3A

-0.00616

(0.00.584) -0.01761

(0.00520) -0.02040

(0.00491) -0.02091

(0.00701) -0.00912

(0.00737)

C4AF

*- 0.00096

(0.00163) -0.002184

(0.001382) -0.002171

(0.001295) *-0. 002131

(0.002,357) -0.002686

(0.001456)

Si02

-0.00831

(0.00416) -0.00827

(0.00460) -0.01002

(0.00787) *- 0.00405

(0.00519)

AI2O3

-0.04420

(0.01119) -0.04723

(0.01093) -0.05521

(0.01562) ^-0.00953

(0.01929)

' 153 cements. Avg = 0.2228; S.D. = 0.03937. 2 77 cements. ^ 76 cements. * Coet./a.d. ratio less than 1.

12
2Jt hr in moist-air storage) of neat-cement bars of normal consistency made of AE +NAE

pendent variables {SH28)

K20 SO3 C3A/SO3 AljOj/SOa APF Air, 1:4 mortar Ba P Zn Rb Wi S.D.

*+0.0013

(0.0021)

0 . 03983

+0.04390

(0.02544) +0.07160

(0.02432) +0.07198

(0.02310) +0.06632

(0.02794) +0.08792

(0.04916) +0.08251

(0.02923) +0.08873

(0.02995) +0.06113

(0.03508) +0.18688

(0.06774)

+0.01095

(0.01041) +0.0.3038 (0.00939) +0.03279

(0.00892) +0.03077

(0.01061) + 0.03841

(o! 01885)

0.03829

+0.08193

(0.01434) +0.06879

(0.01476) +0.07933

(0.02065) +0.06265

(0.02287) +0.08333

(0.01264) + 0.06610

(0.01480) +0.06999

(0.02150) +0.05808

(0.02220)

+0.0000072

(0.0000060) +0.0000106

(0.0000058) +0.0000160

(0.0000087) *+ 0.0000074

(0.0000089)

+0.00087

(0.00074) +0.00112

(0.00071) *+0. 00071

(0.00105) +0.00122

(0.00103)

0.03217

+0.2887

(0.0957) +0.3222

(0. 1085) +0.2746

(0.2294)

+0.044.54 (0.02202) +0.07274

(0.02754>

* +0. 00272

(0.04030)

-0.09902

(0.09034)

* +0.02507

(0. 16517) — 0. 1283

(0.1189)

+ 2.910

(1.477) *+ 1.845

(1.127) +3.210

(2.214)

0.0.3050

0.02967

^ 0.03244

+0.05713

(0.01950) +0.06750

(0.01929) +0.05064

(0.02275) +0.12983

(0.04293)

0.03217

+ 0.0000070

(0.0000062) +0.0000108

(0.0000096) *+0.0000040

(0.0000091)

+0.00122

(0.00071) *+0.00087

(0.00105) +0.00130

(0.00099)

+0.3321

(0.0941) +0..3.331 (0.1073 +0.3765

(0.2134)

+0.04125

(0.02191) +0.07419

(0.02759) *- 0.00819

(0.03840)

+ 3.000

(1.473) *+1.713

(2.135) +3.446

(2.140)

0.03043

0.02967

0.03136

first 24 hr in moist-air storage) of neat-cement bars of normal consistency made of NAE

pendent variables {SH28)

MgO Na20 K20

+0 08421 +0 09857

(0 01636) (0 01361) +0.005386 +0 09205 +0 07790

(0.002268) (0 01543) (0 01449) +0.003992 +0 08144 +0 09711

(0.003523) (0 03045) (0 02339) +0.008647 +0 08983 +0 05078

(0.002813) (0 01526) (0 01676) +0 07881 +0 08667

(0 01600) (0 01291) +0.003919 +0 08770 +0 07347

(0.002478) (0 01516) (0 01453) *+0. 002059 +0 08159 +0 09010

(0.003967) (0 02951) (0 02346) +0.007472 +0 08648 +0 04950

(0.003026) (0 01512) (0 01697)

S03 +0.04961

(0.02601) +0.07168

(0.02399) +0.07884

(0.02260) +0.06935

(0.03229) +0.04069

(0.0,3419) +0.08868

(0.029.33) +0.09543

(0.02920) +0.09186

(0.03802) *+0. 01441

(0.05792)

C3A/SO3

+0.01447

(0.01064) +0.03121

(0.00929) +0.03679

(0.00877) +0.03789

(0.01219) +0.01778

(0.013.54)

AI2O3/SO3

+0.06275

(0.01950) +0.07393

(0.01881) +0.08284

(0.02437) *+0. 01200

(0.03714)

APF

+0.0000094

(0.0000061) +0.0000133

(0.0000057) +0.0000167

(0.0000107) +0.0000111

(0.0000063)

+0.0000094

(0.0000082) +0. 00001 10 (0.0000113) +0.0000095

(0.0000069)

+0.3194

(0.0933) +0.2128

(0.1232) +0.8193

(0.1830)

+0.3441

(0.09.35) +0.2521

(0. 1219) +0.8444

(0.1859)

+0.04893

(0.02137) +0.07777

(0.03130) *+0. 00447

(0.02873)

+0.04897

(0.02138) +0.08081

(0.03074)

* + 0.00241

(0.02916)

Zn

-0.09635

(0.08742) *+0. 07214

(0. 13900) -0. 14922

(0. 10943)

+0.10868

(0.08722) *+0. 06314

(0.13602) -0.14377

(0.11173)

Rb

+3.021

(1.450) +2.412

(2.430) + 2.455

(1.636)

+2.934

(1.452)

* +2.166

(2.383) + 2.482

(1.670)

13
Table 9-12. Calculated contributions of independent variables

to the percentage shrinkage at 28 days (the first 24 hr in moistair-storage) of neat-cement bars of normal consistency

Inde- pendent

variable

C3A CAF**... MgO

NajO

KjO

SO3

C3A/SO3-. APF

BaP

Zn** Bb

Ranges of variables, percent

0 to 15

4 to 17 0 to 5 0 to 0.75 0 to 1.1 1.2 to 3.6

0.4 to 10.1 *2500 to 5500

0 to 0.2 0 to 0.5 0 to 0.2 0 to 0.01

Coefficients from eq 3

table 9-11

-0.0204

-0.00217 +0.00539 +0.0920 +0.0779 +0.0788 +0.0368 + 0.0000133 +0.319 +0.0489 -0.0964 + 3.021

Calculated contri- butions to SH28

Const. = -0.023

0 to -0.306

-0.009 to -0.037

0 to +0.027

0 to +0.069

0 to +0.086 +0.095 to +0.283 +0.015 to +0.372 + 0.033 to +0.073

0 to +0.064

0 to +0.024

0 to -0.019

0 to +0.030

Calculat- ed ranges

of contri- butions to SH2S

0.306 0.028

0.027 0.069 0.086

0.188

0.357

0.040

0.064

0.024 0.019 0.030

*cmVg-

*Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

Ba, Rb, and Ni in eqs 2 and 4, a further significant reduction was obtained. The coef./s.d.

ratio for Rb, however, was less than 2. Equations calculated for the "odds" and "evens" in

the array of cements (eqs 2A, 2B, 4A and 4B)

indicated that C^A, C3S, MgO, C3A/SO3, AI2O3/

SO3, and Rb had coef./s.d. ratios less than 1 in one or more of the equations for the smaller

groups.

A comparable series of equations for the

NAE cements is presented in table 9-15. The

coefficients of the different independent variables agreed fairly well with those of table 9-14

where the AE cements were included. The variables C3A, C3S, and Rb had coef./s.d. ratios of

less than 1 in equation 2A where the "odds" in

the array of cements were used in the computations.

Table 9-13. Frequency distribution of cements with respect to percentage shrinkage of neat cements of normal consistency after 6 months drying in laboratory air after 24 hr moist-air storage {SH6M)

Type cement

Percentage shrinkage

Total

0.16

to 0.20

0.20

to 0.24

0.24

to 0.28

0.28

to 0.32

0.32

to 0.36

0.36

to0.40

0.40

to 0.44

0.44

to 0.48

0.48

to 0.52

0.52

to 0.56

0.56

to 0.60

0.60 and

over

Number of cements

I 2 17 22

422

19

17

14

15

15

12

13

210

1 4

1 1 2 1 778

60

2

19214

lA

II 4 17 2 IIA

III 2 3 IIIA

IV, V 1 4 Total 7 40 66 29 28 3 5 0 1 2 0 1 182

Coefficients of the independent variables in

eq 2 of table 9-15 and their ranges were used

to calculate their contributions and their possible ranges of contributions to the 6-monthskrinkage values of the neat cement bars for

NAE cements. These are presented in table

9-16. The independent variables, C3A/SO3,

Na20, K2O, and Ba, apparently resulted in the

greatest calculated ranges of the contributions

to the 6-month-shrinkage values.

5.5 Time of Cracking of Annular Specimens

Restrained from Shrinkage

The frequency distributions of the time of

cracking of the annular specimens made with

the different portland cements, each using the

water required for normal consistency, are presented in table 9-17. The specimens were

stored in an atmosphere of 95 to 100 percent

relative humidity for the first 24 hr. The time

of cracking ranged from a few minutes to more

than 40 hr after removal from the molds. The

Type I cements had a broad distribution of

values with a large number cracking within a

relatively short time. More than half of the

specimens made with Type III cements also

cracked within 2.5 hr. The median values of

the Types II, IV, and V cements indicated that a longer time period was required for the an- nular specimens made with these cements to crack. There was, however, considerable over- lapping of the distributions of the time of

cracking of the cements of the different types.

Preliminary plots of the time of cracking of

the annular specimens versus various individual independent variables are presented in

figure 9-5. Absolute values of "quadrant sum"

equal to or greater than 11 were obtained for

SiOs, AI0O3, Fe203, SO3, K2O, total alkali, C3A,

C2S, C4AF, and Al203/Fe203.

An outstanding feature of the distribution of

the time-of-cracking data is the large concentration at the early end of the scale. More than , half of the breaks occurred in 10 hr or less. Thus the distribution curve of the data is strongly skewed to the right, i.e., the "hump" , of the curve is near the left end with a long ^ "tail" stretching far out to the right.

14
CO CO

CO tJ- CO 00 1-- CO

lO

O lO 1-1 CO (N TJI CO

1^ CO

00 tT CD oo oo oo

00 CO

4-^

00 -H -rJH 00

r- (M t-- CO 'TO to

CO

CD Oi 00 iC

lO CO

w oo

OS

O 00 -HO ooooo o oo

OO Oi o lO —< o

o: 00 CD C-) — O " -H O O O oo OO o o o o o o o o

CO CD 05 05

05 CD Tf 1/5 O O w

c^ ^ -HO O o o o oo oo o o o o oo oo

Oi CO

(N

O Ot^o ooo o o o ooo o o o o o oo oo oo oo oo oo oo

in o O CD M o oo

O CO 00 o ^ ^ 1^ CO

o: CD

O CO

-H

O -^—i oo oo

oo oo

O 00

CO

lO

—1 o oo

CiOi CO 00

ic Tj^ 00 — o oo oo oo

c; 00 — o oo oo oo oo

r-O

CO CO

CO OOo o

CD CD

M

CO o cm CO CO "<j' o oo oo oo

r-tlO CO »0

Oi CO Tt^ CO O CO Oi -t -<o oo oo00 o ^ ^ Oi -HO o o oo oo

oo oo oo oo oo oo — 00

Oi

(N -H -HO

00O CO

CO Oi CO CO

-H -H CO -HO -HO

(M lO '•3- Ci

00 CO o O OI CO -lO -HO

O (N CO CO

CMW Oi Oi O) -H -H -HO -HO oo oo oo oo oo oo oo

lO o oCO w

-hO

-H 00 O CO Cs) C5 C-1 CO CO -HO — O

to OI 00 00

Oi T}- CM -H 00 OI CO CM oo -hO

c3i CO

-H Oi 00 OI

TJH '-^ 00 CO — O -hO oo oo oo oo o o o o

COCO

TP to

00oo

Oi »0 OI CO

Oi -H

O 00

O Tj- 00 CO " o o o oo oo

oo o o o o

CM

O CM CM CD CD oo

CD lO OI

OI CD 00 Oi

CD lO CO oo oo oo o o o o o o o o

OiCO Ot^ -HO ooo o oo oo oo oo

Oi lO

a>

CMCO Oi ooo o

CM

O Oi Oi

lO CO

»0 lO -<J< CM

CM o o o o o o o o

00 CD

00 o 01 -HCO ooo o oo ooI ^ oo oo

00 to CM Oi

01 CO oo

Oi Oi Oi Oi CO CM

-H CO

O CO oo oo oo

II II oo+^

II II oo

15 -c X-6

ooI 2CD ^ 00

(O CO

CM ^

rolOO ^ CN 4-^

(N CO

CO <N OO oo

CO

CO Gi

to 00

ox o ooo o o o oo

oo

00 0 CD

01 o o c CO

c: CD X—'O OO

OO

a-o

T^ CO

IN C>J -< o ooO Tj< CO

cr. (N oo

ooo ^

CO

CO iC ^ooo

4413

2970;

,6951

273i;

4654 4437;

,8738

3581) o o1 ^ oo1 ~^

II II II II II 11 II II

X-c

EC CO

CaOK^ s

-srS S

Oi42

«3on<

E-i

10 CO

iO o oxCiX

CO iC XCD

(O o o 10 XCD X O

X fO X o 0J05

CO (N (N CO CO

1-1 10 t-<

CO r-- ^ a;

(N '-' t-- CM

c-1 OJ o 00 00

CD Oi

CD

Tf 00 INO CO O CI O »o

CI CI CO

CO (M CD CD lOO

lO

W •-'CO Oi^ Oi O WO CO O)

CO <N CO CO CO (N 4.- O Oi X to

to

iM lO Oi 0>

<N CD CO 00 00

Oio CO Oi s§00

-H CO

CM

CM 00

CMO

OO

Oo o o o

00 cs CO t-^ CD —<

OJ -H o o o o o o o o

00 Oi

^- CO

Ol o o o o o o o o

CM CO

CD Oi

CM 1^

-H

O o o o o o o o o

Tj- OJ

10 CM

CM

O 00o o o o o o

-H -H

Tji CD lO Oi

CO

O Oi o 01 ^ -H -H 00 00

00

00 00 o o 00 00 00 00

-H Tt< CM Oi Oco 01 CO

-H

O 00

iO lO CM Oi O CD CO Oi

-H ^ CM o 00 00

00 00 00 00

-H

O 00

00 CD "* O — o 00

01 CM

01 Oio o o

LO CO

-H Tji Oi CO

-H

O 00

00 00 00

Tp HH Oi Tti CO 0000

Oi -H 00 CO o o 00

CC LO 00 -H

CJi »o 00

00 CM <3i CO

CD »0 CO -H 01 LO TlH 00 -H O 00

CO 00 CO CO CO

CD LO -HO -HO 00 00

00 00 00 00 00 00 00 00

CO o CM CM -HO

Oi -HCO o TM -H O

TlH CM

00

-H CM

-H

O

-H 10 cooo

iC 00 00

CO

—' CM —10 — o

OI T)* 000 TJHCO CM CM CM CM -HO -HO 00 00 00 00 00 00 00

CO CM

CO CM

-H

O

01 CM

Oi

O CO CM — o

CD

t~ CM

CO -HO

Oi

O

CM

CM -hO

X TP -H

Tjl CM -HO

CO CM CM "O -HO

CO Tp Oi 00

CM CM 01 CD

00 CO -H CM -HO -HO 00 00 o o 00 00 00 00

OCD O)

O 10 CD CO CN 00 TP ^ TP 00 — o 00

OI -H CO

00 CO CO o CO to CO 00 -HO 00

00 00 00 00

to Ci

TP CO

CD CD 0000o oCD to O O OC

-H

O CO Oi — 00 00o o 00

-H CO

CO -H

Tp 00 — o o o o o 00 00 00 00

CO CO

CO -H

CM Oi

CM 00o o

00

OI -H O CO

CO CM 00o o

TP OJ 000

-H CD

00 00

CMO LO TPCO 00

00 00I ^ 00

Oi to

CO 00 OCO O O

00 O! CO to O to o o

Tp 00 to Tp CO to 00 CD

-H TP OOCD CD ocn too cMr^ -HO ouo

TJ* CO CM to Tp Oi ^ o o

II II 00 00

S-o

CC

K

00 00I ^ 00 00 00m CO

15
The multivariate analysis used throughout

this series of articles is based on the assumption that the underlying distribution curve of

the data is the familiar bell-shaped normal

curve, with the hump in the middle and approximately symmetrical tails stretching out on both sides. In cases where both the data

themselves and logical considerations related to the underlying phenomenon indicate that this

is not the case, some other way of evaluating

the relationships involved must be found if the

results are to be meaningful.

Frequently, when data are not normally distributed, the log or square root or some other

transformation of the original data fits the

normal distribution more closely and can be

handled with the usual statistical techniques

Table 9-17. Frequency distribution of the cements with respect to the time required for the annular specimens of neat cement to crack {TOBR)

Type cement

Time of cracking, hours

Total

0

to

2.5

2.5 to

5.0

5.0

to

7.5

7.5 to 10.0

10.0

to 12.5

12.5

to 15.0

15.0

to

17.5

17.5 to 20.020.0

to 22.5

22.5

to 25.0

25.0

to 27.5

27.5

to 30.0

30.0 and

over

Number of cements

I 193

1

12

17

8 6

19

1

1

8

3

7

o 3 4 3 1 2 1 1 77

8

59

219

214

lAn 7 5 14

1 4 2 I 2 IIA m 10

2

1 4 2 1 niA

IV, V 1

19

3 3 2 2 1 2

Total 35 21 19 23 17 20 11 5 1 4 3 3 181

SHRINKAGE TEST

INDEPENDENT VARIABLES

NOIb Si 02 MZOZ FeaOs CqO MgO SO3 NoaO K2O TOTAL

ALKALI C3A C3S CgS C4AF S A+F

AIR,P, FINE. WAGN

FINE.

AIR

l:4IM0R

TOBR

(1)

(2)

(3) (4)

102 1/

L +17

84 K

NL

-14

102 1/

L? + 14

6

6

NO + 2

84 |\

L?-9

102 KNL

-16

9

3 k

NL

-6

102 k

NL

-19

102 kNL

-16

10 iC

NL

-15

84 k

L? -8

102 kNL

+ 13

10 l>

L?

+ 16

102 kNL

-17

102 kL? + 9

84 kNL

-7

8

L?

-6

8 IV

NL

-9

SH BR

(1)

(2)

(3)

(4)

102 1/

L +13

8

4

NL

-1

84 1/

L? + 7

84 1/

L? + 7

102 |\

L?

-16

102 kNL

-14

8

1 4

L? -2

12

L -24

120 kL -24

9

3 kNL

-9

84 kNO

-2

84 kL? +6

8 1>

L?+6

84 kL-6

84 kL?

+ 8

84 kNL

-12

6

6

NO-4

9

3 k

L?-7

SHBR/SH07

or SB/S7

(1)

(2)

(3)

(4)

10 l>

L +20

102

NL

-II

102

L? + 9

8

L? + 7

84 |\

L? -13

12 l<

L -24

84 N

-6

10 l<

L -19

10 l<

L -20

10 l<

L

-II

8 1^

L? -3

10 0NL + 14

10 \>

L?

+16

8

L?

-10

10 \>

L?

+13

10 1^

NL

-16

8 KL?-612 l<

L -24

SHBR/SH28

or SB/S28

(1)

12)

(3) (4)

84 1/

L

+12

8

4 |\

L?

-12

102 UNL

+13

102 \/

L + 4

102 |\

L -10

102 l\

L -16

84 kNL-9

12 1^

L -24

102 kL -20

84 kNL

-12

6

6 kNO

-6

84 kNL + 12

8 l>

L? + 11

84 kL?

-II

8 l>

L? +11

9

3 kNL

-II

84 kL? -810

L

-16

Figure 9-5. Results of plotting (1) the time of cracking of the annular specimens, (2) the percentage shrinkage of prisms at the time of cracking of the annular specimens, and (3) (U) the ratios of the percentage nonrestrained

shrinkage at the time of cracking of the annular specimens to the nonrestrained shrinkage at 7 and 28 days, re- spectively, on the "Y" axis versus various independent variables on the "X" axis.

* Note (1) Ratio of number of plotted points in pairs of diametrically opposite quadrants. Note (2) General trend of lines drawn through plotted points. Note (3) Apparent nature of relationship. L = linear: NL = nonlinear; NO = no apparent relationship; and L? = nature of relar tionship not determinable. Note (4) Quadrant sum in corner test (see reference 5).

Table 9-16. Calculated contributions of independent variables

to the percentage shrinkage at 6 months (the first 34 hr in moist-air-storage) of neat-cement bars of normal consistency

{SH6M)

Inde- pendent

variable

Ranges of variables, percent

Coefficients from eq 2

table 9-15

Calculated contri- butions to 81128

Calculat- ed ranges

of contri- butions to SH6M

Const. = +0.004 O3A 0 to 15 -0.00603 0 to —0.090 0.090 C3S** 30 to 70 +0.000669 +0.020 to +0.047 0.027 NajO 0 to 0.75 +0.139 0 to +0.104 0.104 KjO 0 to 1.1 +0.123 U to "T U. 1 oO \j. loo MgO 0 to 5 +0.00879 0 to +0.044 0.044 C3A/SO3-- 0.4 to 10.1 +0.0175 +0.007 to +0.177 0.170 APF *2500 to 5500 + 0.0000224 + 0.056 to +0.123 0.067 Ba 0 to 0.2 + 0.575 0 to +0.115 0.115 Rb** 0 to 0.01 +3.686 0 to +0.037 0.037 Ni 0 to 0.02 +2.617 0 to +0.052 0.052

*cmVg.

**Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

16
[18]. Of several different functions of the

time-of-break-data tried, the square root gave

the best approximation to a normal distribution. Table 9-18 gives the frequency distribution of the square root of the time-of-breakdata by types.

Table 9-18. Frequency distribution of cements with respect to the square root of the time required for the annular specimens

of neat cement to crack (TOBR) "-^

Siiuare root of time of break in hours

0 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 Type to to to to to to to to to Total

0.75 1.50 2.25 3.00 3.75 4:50 5.25 G.OO 6.75

Number of cements

I 4 15 12 13 15 10 6 1 1 77 lA 3 1 1 3 8 n 1 7 14 13 19 3 2 59 IIA 1 1 2 m 4 6 2 3 3 1 19 IIIA 2 2 IV, V 1 6 4 1 2 14

Total 9 26 22 33 40 35 10 5 1 181

Selected equations relating various independent variables with the square root of time of

break are given in table 9-19 for AE + NAE

cements and in table 9-20 for NAE cements

alone.i" Equation 1 of table 9-19 indicates that

specimens made with cements with the higher

water requirements for normal consistency

(Wi) had a tendency to crack earlier than those

with lower water requirements. The relationship of commonly determined variables to the

time of break is presented in eq 2. The S.D.

value was reduced very significantly (see table

9-34). With the addition of the independent

variables MgO, Ba, Rb, and Zr in eq 3 a further

significant reduction in variance was attained.

In the equations for the "odds" and "evens",

SO3 in eq 3A and Rb and Zr in eq 3B had coef./

s.d. ratios less than 1. The use of the oxides

Si02 and Fe203 in eqs 4 and 5 resulted in S.D.

values almost identical with those attained in

eqs 2 and 3 when the calculated compounds C3S

and C4AF were used.

" Since the analysis of this subsection is based on the square root of the time-of-break-data, the various statistical quantities calculated such as coefficients, standard deviations, etc., cannot be used

directly as quantitative measures of significance associated v?itb the original untransformed data. However, since the square root transformation is order-preserving", relative matjnitudes and

trends of these measures may be used to support the general re- marks about relationship given here. It is interesting that, al- though the coefficients and standard deviations were changed by the transformation of the data, coef./s.d. ratios were almost the same

for the square root as for the untransformed data.

TIME OF BREAK, HOURS (TOBR)

Figure 9-6. Results of plotting the percentage shrinkage of the nonrestrained bars at the time of cracking of the annular specimens versus

the time of cracking of the annular specimens.

(Both types of specimens were made of neat Portland cement pastes of normal consistency and cured for 24 hours in moist air prior to exposure to laboratory air.)

Corresponding equations for the NAE ce- nients are presented in table 9-20. The coeffi- cients for the different independent variables

and the coef,/s.d. ratios were in reasonable

agreement with those of table 9-19 where the

AE cements were included.

Coefficients of the variables in eq 8 of table

9-20 were used with their ranges to calculate

17
coco (NO dd

(N 1-H CC rH CO T}1

ICO l^"^ Ol CD ood ooco oi>

00 Cfl Tt* l>iM

cooo o

lOO

CO

00 (N

a>^ cooo ai CO oco c:co aio »0(n (Nco

(Mtji coco 00^ ocas ^ '-f ^ <j) T-* oooi

lO ^ T-H (M lO ^ r-- CO T-H lOC^ CD ^ CO oo oo oo oo oo oo oo +^ +"-' +^ +^

r-H Oi lO O COt^ <J><J> t^-^ tMOO ^CD

t^cD --^CO 0> (N CO Tt^ (M-tP rH coai 00^ (SI O; O rH ^ rH C^l hH I-H oo oo -HO oo rHO rHO rH O -HO oo oo oo OO OO oo OO CO oo oo oo OO oo CO oo oo

od dc dd dd dd dd dd dd 1"^ 1"^ 1^ I-" I'"' I"" I""' I"""

(NIC Tj^OO (NOO C^S" rHU? OOrn --^ CCD

tH CO coco t^iO CilO coco coco COlO CIO

(Md Wd rHo' (Nd NO (NO rHO COO I" I"" I"" I"" 1^ I""" I"""

lOrH I-H05 rHOi OOCO COrH t^Ci t^l^ t^rH

io coco t^cD »o CO coco coo

rtd l-HC r-IC rHO O rn'd O rnd IW I" 1^ I" 1^ l- I""

dd

C3i»C COC NOi X CO O TP CD »0 CO(N (NCO TjiCO OO oc oo

W5 1^

rH lO rHO

tH C4

00 lO COO

rH ^ lO rH COi CO

I OO ooI ^

O CO

Oi o

id 00 0:00

T)< O

CCD COOO

CO CO O rH iCrH lOrH OO oo oc CO

00 Tit CJCO

COCO (N

TfH CD (NO O lO rH * C rH

rH O) CO Ol NO <MC OC oo oc cc

CO o CO CO rHO

OOCO

00 05

CO N rHO

CO >o

in

lO -at rHO

CO (M t>o

CO Tjl rHO OO OO oo

lOO

(N rH OO (N rH CC

CO cc cc cc

O) 00 IN CD COCO 1-HTf CO OS05 00 cs f^CO 00 1^ cot^ ooc CRrH CDt^ OICD

00 rH too CDC IC rH CO rH OrH rH N rH (M +

^ +^ +^

U U 11 U II II II II II U II II II II U II

IN

II M

><

O-d O-a O-a" Ot3 O-d

- H B H » H « H I

-

§•2

a.

s

S ^

ft; cq. O

^£

C ~H. s .«

rCI

"5^ « "-^ ^ e

CO

3

05

mH

lOOO

IN CD a c dd

I '-'

CO rH

I ^ CO (NI ^

m-^ i-H.* i-ico CD03 COOO coco

OOM t^lO t~ IN

I ^

CO rH

I CON rHW

C0-4t COX X-"*!

ION CN

I

t~ N

I Cl^

i-HTjl rJ<..H, N NX tON XX 05O NTfl OrH O f-l ION CON IC rH OCO lOI^ x^t

00^.^ rH« OO O rH CD N N CO OC OC OO OC +^ +^ OC CO CO

NOl NO XCO CDCO t^CO COOi 05 CO XO rHt^ Nt^ C O) rH COO tJI t^H Oi <J> Oi rH OrH NCO ON OrH rH CON OrH CO rHO rHO CO rHO -H O rH O rHO CC OC CO CO oo OO oo oo CO oo oo oc oc CO oo oc

CO

I oo oo ocI " I ^ oc CO oo cc

CO CD WC NO rHOS Ot^ t^O 050 Xt^

t^CO N TJi Oi CD coo CDCO rH Tjt coco OO

NO NO rHO NO NC Nd rH d NO

I"' I" I" 1^ I"-' I"" I"-' l^-"

rHC? --tC nS" ^n" Xn" OiC NoT O OTP Otjh tncD -^O COtji COtJH coco no

rnd r-Id rn'd rHO rHO -io l-io rHC

I-' 1^ I"" I"" 1"^ I"" l'^

Nt^ CON CO rHO

TJto CD-* --^HX TJICO CON NN rHCO NCO CC

I ^ OO CO ocI ^

oo CON COO

rH tH IN M rH tPCD tJhC XX rHC NrH CO

d d d d d d

CO -f-H ON t^rH OCO rHO

rH O N rH

I^CO ONciJX CC

OO OO

I

OC

I

TfO

CO o XOi *o

NX XO CO! ox rHX t^Tjl O O CO rH N

rH COrH CC oc oc oo

rHN o^~

Oi CD rHC O rH Tjt O CD O ox rH CD O 05 NC NO

OOi

cox oxNO

CC cc CO

rH O rH O ON OO XrH

Tit CO Tit CO 05 O rHC r-O "C

t^CO

T)l O CTlt rHO CC CO cc oo

oi

Tjt rH o CO o rH CO Oi CD N rH C>J rH CM rH OO OO oo

d d d d d d +^

oodd

cox

OCO

-at rH t^x

Tjt Nt^

T*t O OrH cj>o

rH r-H CO TP XX CD 1*

CO CD

Tj< Tjl XTJt XrH oo CO O +

" CD rH CD rH +^ +^ +^ N N +^

rH N +^

II II y u U U II 11 II II II u U U II u II 11

(PP' (even; )dd) (even)

)BR) BR) BR) BR) BR) n

BR) BR) BR) Ot3 o-a O-a Ot3 O-c O-d O-d O-d O-d

18
their contributions to the time of breaking of

the annular specimens as well as the ranges of

these contributions. The results of these calculations are presented in table 9-21. Differences

in fineness and K2O appear to have the greatest

effect on the time of breaking with restrained

shrinkage. Increases in fineness, K2O, Na^O,

Ba, and possibly MgO, SO3, Zr, and Rb appear

associated with a decrease in the time of breaking. Increases in loss on ignition and C4AF appear associated with an increase in the time of

breaking.

Table 9-21. Calculated contributions to the time of breaking

(TOBR) o-s of the annular specimens (after initial £4 nioist- air-storage) of neat-cement of normal consistency

Inde- pendent

variable

C2S CiAF... Mg0__.

SO3**—

NaaO.-, K2O

APF____

Loss BaRb

Zr**

Ranges of variables, percent

5 to 50

4 to 17 0 to 5.0

1.2 to 3.6 0 to 0.75 0 to 1.] *2500 to 5500

0.3 to 3.6 0 to 0.2 0 to 0.01 0 to 0.5

Coefficients from eq 3 table 9-20

+0. +0. -0.

-0. -1.

-2. -0. + 0.

0307

1455

1475 266 54

27001022

.544 94

5 -2.1

Calculated contri- butions to (TOBR)»i

Const. = + 0.15 to +0.58 to 0 to -0.32 to 0 to 0 to -2.55 to +0.16 to 0 to 0 to 0 to

+ 6.24 + 1.54 + 2.47 -0.74 -0.96

-1.15 -2.50

-5.62 + 1.96 - 1.79 -0.96

-1.44

Calculat- ed ranges

of contri- butions to (T0BR)»-5

1.39

1.89 0.73 0.64

1.15 2.50

3.07

1.80

1.79 0.96

1.44

5.6. Nonrestrained Shrinkage of Prisms at

Time of Cracking of Annular Specimens

A plot of the percent shrinkage of the nonrestrained bars at the time of cracking of the

annular specimens versus the time of cracking

of the annular specimens restrained from

shrinkage is presented in figure 9-6. Some

of the annular specimens cracked at a time

when the nonrestrained specimens had shrunk

very little. With other cements, the neat pastes were apparently more capable of adjusting to the stresses, or the shrinkage occurred at a slower rate, and a longer period of time was

required to crack the specimens restrained

from shrinkage. No measurements were made

of the loss of weight of the specimens with time

of exposure to the laboratory air. The frequency distributions (for the different types of cements) of the percentage shrinkage of the nonrestrained bars at the time of

cracking of the restrained annular specimens

are presented in table 9-22 The range of the

percentage-shrinkage values was quite broad

for each of the different types of cements as

classified, and there was an overlapping of the

values for the cements within the different

types.

*cmVg.

**Coefficient of doubtful significance as coef./s.d. ratio, was less than 2. ^ Since these data appear to have a reasonably normal distribution, they are analyzed in the usual way.

Table 9-22. Frequency distribution of cements with respect to percentage shrinkage of neat cement bars at the time of breaking of the annular specimens (SHBR)

Type cement

IIA-... n

HA...

ni_... niA-.

IV, V.

Total.

0.005

to 0.010

Percentage shrinkage

0.010

to 0.015

0.015

to 0.020

0.020

to 0.025

0.025

to 0.030

0.030

to 0.035

0.035

to 0.040

0.040

to 0.045

0.045

to 0.050

0.050

to 0.055

0.055

to 0.060

0.060 0.065

to and

0.065 over

Number of cements

13

1

18 12

10

13

"'§'

12

20 15

10

215

1 14

26 21

Total

748

58

2

192

14

177

The results of the preliminary plots of the

nonrestrained shrinkage of the bars at the time

of cracking of the annular specimens which

were restrained versus the various individual

independent variables are presented in figure

9-5. The absolute value of the quadrant sum

was 11 or greater for SiOo, AI2O3, MgO, SOa,

K2O, total alkali, and fineness. Comparing the

signs of the quadrant sums as well as the general trend of the lines drawn through the plotted points with those obtained for the shrinkage at 24 hr (SH24) in the top group of figures

in figure 9-4, it may be noted that, where comparable, the slopes and signs were different for

practically every one of the variables.

Equations relating various independent variables to the nonrestrained shrinkage of the

neat cement bars at the time of cracking of the

annular specimens for AE + NAE cements are presented in table 9-23. The relationship to the

percentage water required for normal consistency, W], in eq 1 was not highly significant.

With the use of commonly determined variables

in eqs 2 or 4 there was a highly significant re- duction in the S.D. value (see table 9-34). The

use of the trace elements Rb, Ti, Cu, and V in

eq 3 or Rb, Cu, and V in eq 5 resulted in a

reduction of the S.D. value significant at the 5-

19
CO CO

00 lO CO CO

!NO

CDOO

doI ^

too OO

CD CD OOOO

do

00 00

CD

00 --J^ ^ lO

lOOOo o dd dd

lO ooO O

CDO ooOO

ddI

OOO O o o OO

ddI ^

lO 00

IC CD " O OO

ddI "

CO CD

(M «O O O OOO O ddI ^

oo^ o lO 00

CO ^ ddI ^

CD <N

OOI ^

-<o

01 Oi oo

dd

00 00 00o oooo

ddI ^

in *

O-i

wcD rtO ddI

00 Ol

Ci o^

ddI -"

CD CO oCO 00O OO

dd+'~^

CO Oi CD CD dd

CO

CD C^l OOOO

dd

t^o O -I o -< o o oo

ddI ~"

WO'O 00 »0 CO C: Tf -—CD lO

CI CO 00 CO OO OO OO

OOI OO ^ ^ ^ Tj< 00 (N Tt- lO CO O CD lO (NO lO CD lO OOI — OO oo

CJlO iO

O lO

O lO

lO " O O o o OO oo

dd dd +"

CM CD CD CD O ^ O oo OO O O O O

IC CO Oi

CD CD CO -<d dd O CO CO --^ ooo oo O ^ CO oo oo oo

oo

CD ^ lO ^

CD o; o >-< CM O O " oo OO OO OO

OOI ^ OO ooI ^ o o

00 00 --H o o o o o o o oo

ddI ^

OM— o ooo o oooo

ddI ^

cnco -^cD ^ T-i CM ^

rtO -HO oo OO oo oo o o o o o o o o

00 00 CO a;

CO --I

O CI

O " o OO oo o o o o o o o o o o o o oo ooI ^ ooI ^ ooI ^

CM 05

lO CO

CM

O oo

CD

CD

CMO oo

05— o oo

lO Oi

o> ^

CO

CO o oo

OO CO lO

CD

O

CI

O Ol o O O O

^00 00 o; O (MCD

Ol CD <N — O coo OO oo

ooI ^ ooI ^ oo oo ooI ^ ooI ^ oo

CO

-H

O o o

CO"Ooo

ooo

lO o 00 CD ooo o

00 00

00 CD

a; y-< lO 00

CM lOW "'J' rji CD TT< ~ O —' o oo oo

Tt< CJ Ot^

»0(M OCD

CD CO CD

OO CM

O OO oo

oo ooI oo oo ooI ^ oo

CO ^CO OOCD

OiOO CM 00 oo ^ o oo

CO

CIX

»OC0 ooi ^ oo oo

CO CM CO CO ^ CI ooo o o o

CD CM o o o o o oto CO o o oooo

oooooo

ooI - oo oo oo

CO

OO -H lO CM ^ o:

Oi CD CI lO

CD CTt

O oo OO

"OXXCD

Ol o OO

CD CD

CM CO COX oo" o

CO CI X ^ oo

OTP CO

Oi o oo

CO ^ CO CO CO Tf X CD CD ^ Oi CD CM

OOOO o; ^

rtO "O OO

oo oo oo o o o o

II II II II

K-6

oo oo

P3 . pq ,

oo

a; m

t/i oi s

13soI Hm<

»OlC

CM CDo oo

ddI ^

oodd+^

cox

coco rfO ooddI

oo

ddI ^

05CD oo

CM

O oo

ddI ~'

lO CO lOTp oodd

COXtP

Tp

O

ddI ^

lOO

TPOlO

CO TP

TP

TP ^ OOoo

dd

CI 00 O CD CIO oooo

ddI ^

ooo o o o oo

ddI '~' o cJ

OS CD

CM Tp ooooddI ^

xoWO) ooo

dd

oo

»o o X-i

MCD dd

CO o CO CM oo

dd+"

COiO ooCM w ooddI ^

oo

ddI oin

oco

CM

CM

O oo

ddI 

XX0> lO oo

ddI ~-'

OiCMOi XCD

CO t-i

WCM

CO i-H CD CJi OCD dcI

OOi <i*^

CO »0 CO lO

»0

O Tp

w oo oo oo oo

oo oo

coio cox X C^i CD CD ,-hO •-IO oo oo oo oo ooI ^ oo

rtX i-icD O O O w — O -HO oo oo oo ooI ^

"^r^ oco Xt^ COi-t CD CO iO oo oooo

oo oo

lO

Ti^ TP ^tP ooddI ^

lO o CO Tp -H O O -H ddI '-'

CD CO

TP

O) CD

to TP ddI ^

Oi CD o »o oo

dd+^

ooI ^

ooo o oo

ddI

TP TP o o oo

ddI 

O -P -H X O CO CD

-H

X lo oo oo

ooI oo ^

CD

w to

X

O

w CO Oi

1^ to TP o -H -H CO -H dd dd o

TP

X CO to

Oi CO dd

oo

oo

oo

TP O)

TP TP CD TP -HO oo

cDc:i O- TP n^ TP -HO CO

CO to

Oi CO

-H

X

— o oo

COtP CDO

O)X XtO

l^to CD Tp -HO -HO oo OO

t;0

CD to

to Tp S8

ooI ^ ooI ^ ooI ^ oo ooI ^ oo ooI ^

OiX oo

O :d tOf^

CMX ooI ^ oo ooI ^

XtP

COCO

Tp

O oooo

CO TP CDO oooo

C31 -H TP O rP TP oo

-H

to

w

Oi TP oo

ooI ^ oo CO COI ^

Oi I>

TP -H o o CMddI ^

CO CJi to T-H r~ c X CO

CO

O TP o oo CO oo ooo o ox Tp CO X O X Oi

-H -H -HO o o o o o o o o ooI X 'H CO X o o o — O -HO O C O O o c o c o o o c CO CO

CO

-Hto OCD

CO CO Oi

TP CD CD o o o c O O CO

dd dd

Oi Oi O) CO c CO o c:i CO X X to -HO -HO CO o o OO

too oo to CD CD CO O O TP CO O -H O -H o o o o O C CO

oo

tot^ coo

CD CD CO CD CO -H c^i O CO oo

coco Oco CO"O 0 o

01 Oi

Oi c oo

t>- CO to Oi oo toco Or-* OiO -iC oo

Oi

O -H c X -H -H CU -H O C O) -H C w

-I

O CO -HO CO

II II

OS

m

oo

cq

03 CO

oo

Pi

ffl

oo

11 II

Pi

oo

Pi« .

oo+^

IIu

Pi

CO CO

CO CO+- U II II II OO

II II

Pim

K-6

CO CO

Pi

pq . m .

20
percent probability level. In the equations for

the "odds" and "evens" (eqs 3A, 3B, 5A, and

5B) the coef./s.d. ratios of MgO, Rb, and V

were less than 1 in one or the other of the

equations for the smaller groups of cements,

and the coefficient for Ti had a reversal of

sign in eq 3B.

Corresponding equations for the NAE ce- ments are presented in table 9-24. The coeffi- cients and coef./s.d. ratios of the independent

variables are generally in accord with those of

the previous table where the AE cements were

included. In table 9-24, the coef./s.d. ratio for

Ti was less than 1 when included with the other

variables in eq 3. As in the previous table, the

use of commonly determined variables in eqs 2

and 4 resulted in a highly significant reduction

in the S.D. values. The additional use of the

trace elements in eqs 3 and 5 did not result in

highly significant reductions in the S.D. values

(see table 9-34). The equations for the "odds"

and "evens" (eqs 3A, 3B, 5A and 5B) indicated that the coef./s.d. ratios of AI2O3, Rb,

and V were less than 1 in one or the other of

the pairs of equations for the smaller groups

of cement.

Using the values for the coefficients of the

independent variables in eq 3 of table 9-24 and

the ranges of these variables, calculations were

Table 9-25. Calculated contributions to the -percentage shrinkage

of neat-cement bars at the time of cracking of the annular

specimens (SHBR)

Calculat- Inde- Ranges of Coefficients Calculated contri- ed ranges pendent variables, from eq 3 butions to SHBR of contri- variable percent table 9-24 butions to SHBR

Const. = -F0.101 CsA 0 to 15 -0.000673 0 to -0.010 0.010 Na20 0 to 0.75 -0.01496 0 to -0.011 0.01

1

K2O 0 to 1.1 -0.0229 0 to -0.025 0.025 APF *2500 to 5500 -0.0000124 -0.025 to -0.068 0.043 MgO 0 to 5.0 - 0.00202 0 to -0.010 0.010 Loss 0.3 to 3.6 +0.00414 +0.001 to +0.015 0.014 Rb** 0 to 0.01 -0.6045 0 to - 0.060 0.060 Cu 0 to 0.05 -0.2483 0 to -0.012 0.012 V** 0 to 0.1 -0.0555 0 to -0.006 0.006

*cmVg.

Coefficient of doubtful significance as coef./s.d. ratio was le.ss tlian 2.

made of their possible contributions to SHBR

and the ranges of their contributions. These

calculated values are presented in table 9-25.

Differences in fineness and K2O appear to have

the greatest effect on the nonrestrained shrinkage of the bars at the time of breaking of the

restrained annular specimens. Increases in

Na20, C3A, MgO and Cu may also be associated

with lower values for SHBR but increases in

the loss on ignition with higher values.

5.7. Ratio of Nonrestrained Shrinkage at Time

of Cracking of Annular Specimens to the

Nonrestrained Shrinkage at 7 Days, (SB/S7)

The frequency distributions of the different

types of cements with respect to the ratios of

the nonrestrained percentage-shrinkage values

(SHBR/SH07) or SB/S7 are presented in

table 9-26. The shrinkage ratios varied over a wide range,—from 0.02 to over 0.54—indicating that the annular specimens of some cements

cracked when very little shrinkage had oc- curred in the bars, and others only after con- siderably more shrinkage had occurred. This

difference is, however, further complicated by

the fact that the rate of shrinkage was not the same for all cement pastes as was noted in

figure 9-7.

The results of plotting SB/S7 versus the

various independent variables are presented in

Fig. 9-5. The variables SiOs, AI0O3, MgO, SO3,

KoO, total alkali, C3A, CoS, C4AF, S/(A + F),

air permeability fineness and (air, 1 : 4 mortar)

all had absolute values of 11 or more for the

"quadrant-sum."

Selected equations are presented in table

9-27 to indicate the relationships of the combinations of independent variables to the ratios

of the nonrestrained shrinkage at the time of

cracking of the annular specimens divided by

the nonrestrained shrinkage at 7 days for the

AE 4- NAE cements. The relationship in eq 1 indicates that the shrinkage ratios are probably

lower with higher water-requirements for nor- mal consistency. Table 9-34 indicates that the

Table 9-26. Frequency distribution of the cements with respect to the ratio of the shrinkage of the neat cement bars at the time of crack ing of the annular specimens to their shrinkage at 7 days {SHBR/SH07 or SB/S7)

Shrinkage ratio

0.02 0.06 0.10 0.14 0.18 0.22 0.26 0.30 0.34 0.38 0.42 0.46 0.50 0.54 Type cement to to to to to to to to to to to to to and Total

0.06 0.10 0.14 0.18 0.22 0.26 0.30 0.34 0.38 0.42 0.46 0.50 0.54 over

Number of cements

I 1 10 10 8 8 5 10 7 4 2 2 1 4 1 73 lA 1 2 1 1 2 1 8

II 2 7 4 9 10 12 8 3 3 58 IIA 1 1 2

III 2 4 4 2 1 3 1 1 1 19 IIIA 1 1 2

IV, V 2 2 2 2 2 i 2 i 14

Total 3 17 17 19 17 21 23 22 15 8 5 3 5 1 176

21
Table 9-27. Coefficients for equations for AE+NAE cements relating the ratio of the shrink

of the bars at 7 days (SHBR/SHO?), or

Equation Note Const. C2S C4AF CaO FesOs

(')

(')

(')

C-)

(')

(•)

(')

(')

(»)

SB/S7 =+0.6197

s.d. = (0.1418) SB/S7 =+0.6546

s.d. = (0.0687) SB/S7 =+0.6754

B.d. = (0.0666) SB/S7 (odd) = +0.7251

s.d. = (0.0931) SB/S7 (even) = +0.6727

s.d. = (0.1056) SB/S7 = + 1.827

s.d. = (0.679) SB/S7 = + 1.980

s.d. = (0.655) SB/S7 (odd) =+1.797

s.d. = (0.884) SB/S7 (even) = +1.893

s.d. = (1.036)

*+ 0.000803

(0.000923) +0.001293

(0.000916) *+0. 001006

(0.001243) *+0. 001121

(0.001445)

+0.00578

(0.00276) +0.00843

(0.00276) +0.00676

(0.00401) +0.00844

(0.00413) -0.01645

(0.00985) -0.01819

(0.00950) -0.01512

(0.01287) -0.01707

(0.01500)

*+0.00657

(0.01072) +0.01433

(0.010.55) *+0. 01079

(0.01504)

* + 0. 01526

(0.01568)

» 167 cements; Avg = 0.2514; S.D. = 0.1125. 2 84 cements. ' 83 cements. * Coef./s.d. ratio less than 1

relationship was significant at the 5-percent

probability level. The use of commonly determined variables in

eq 2 resulted in a highly significant reduction

in the S.D. value. C2S was included although the

coef./s.d. ratio was less than 1 in eq 2 but

greater than 1 in eq 3. With the additional use

of the trace elements, Rb, V, Ni, and Cu in

eq 3, a further significant reduction in the S.D.

value was obtained although none of the coefficients of any of the individual trace elements was by itself highly significant. The coef./s.d.

ratio of CoS, Rb, V, and Cu was less than 1 in

eqs 3A or 3B, or both when the smaller groups

of cements were used in computing the equations.

The use of the oxides in eq 4 instead of the

potential compounds also resulted in a significant reduction in the S.D. value (see table

9-34). With the addition of the trace elements

in eq 5 a further significant reduction was obtained. In the equations for the "odds" and

"evens" (eqs 5A and 5B) the coef./s.d. ratios

of Fe20,3, SO3, Rb, and Cu were less than 1 in one or both of the equations for the smaller

groups of cements and the sign of the coefficient i for V was reversed in eq 5A,

| A corresponding series of relationships computed for the NAE cements is presented in

table 9-28. Equation 1 indicates the relationship of the shrinkage ratios to the water re- quirements for normal consistency of the neat

cement pastes. Equations 2 and 4 present the

relationships of commonly determined variables and eqs 3 and 5 the commonly determined

variables with the addition of trace elements.

In eq 5, SO3 was also used. A highly significant I

22
age of neat-cement bars at the time of cracking for the annular specimens to the shrinkage

SB/S7, to various independent variables

S03 MgO NaiO KjO APF Rb V Ni Cu Wi S.D.

— 0.01488

(0.00572)

0. 1106

-0.01571

(0.00546) -0.01965

(0.00536) -0.02217

(0.00764) -0.02032

(0.00832) -0.02672

(0.00860) -0.03135

(0.00838) -0.03253

(0.01216) -0.03044

(0.01250)

-0.1745

(0.0371) -0.1653

(0.0362) -0. 1523

(0.0457) -0.2346

(0.0662) -0.1869

(0.0381) -0.1773

(0.0372) -0.1632

(0.0475) -0.2425

(0.0665)

-0.2560

(0.0307) -0.2533

(0.0348) -0.2436

(0.0502) -0.2644

(0.0537) -0.2563

(0.0340) -0.2607

(0.0379) -0.2508

(0.0539) -0.2724

(0.0590)

-0.0000821

(0.0000127) -0.0000872

(0.0000123) -0.0000946

(0.0000165) -0.0000802

(0.0000196) -0.0000739

(0.0000142) -0.0000822

(0.0000141) -0.0000945

(0.0000187) -0.0000703

(0.0000230)

0.0783

-5.748

(3.667) -10.406

(5.003) *+0.899

(5.567)

-0.5124

(0.3763) *+0.6035

(0.6778) — 1.0049

(0.4935)

-3.663

(2.176) -5.118

(3.322) — 5 515

(3.260)

-1.798

(0.853) -2.040

(1.237)

* — 0 765

(1.354)

0.0752

0.0731

0.0782

-0.0367

(0.0228) -0.0331

(0.0222) *+0.0127

(0.0320) -0.0408

(0.0328)

0.0778

-5.715

(3.651) -10.687

(5.025) *+1.013

(5.551)

-0.3812

(0.3634) + 0.6916

(0.6646) -0.8362

(0.4853)

-3.772

(2.175) -5.248

(3.362) -5.295

(3.248)

-1.819

(0.851) -1.890

(1.239) -0.941

(1.358)

0.0749

0.0732

0.0780

reduction in the S.D. values was attainecJ by

using the additional independent variables in

the equations (see table 9-34). It may be noted

in tables 9-27 and 9-28 that the coefficients for

Na20, KoO, fineness, and MgO were all highly

significant. An increase in each of these independent variables appeared associated with

lower SB/S7 ratios.

The coefficients of the independent variables

in eq 3 table 9-28 were used together with their

approximate ranges of values to calculate their

contributions to the SB/S7 ratio and the ranges

of these contributions. These values are presented in table 9-29. Differences in fineness and

K2O were associated to the greatest extent with

differences in the SB/S7 ratios. Differences in

NaaO, MgO, C4AF, and Cu may also be associated with differences in the SB/S7 ratios.

5.8. Ratio of Nonrestrained Shrinkage of Bars

at Time of Cracking of The Annular Specimens to the Nonrestrained Shrinkage of the

Bars at 28 Days, (SHBR/SH28) or (SB/S28)

The frequency distributions of the shrinkage-ratio values (SB/S28) of the different

types of cements are presented in table 9-30.

A fairly broad distribution of the shrinkageratio values was obtained with each of the

types of cement as classified. There was also an overlapping of the values in the different

types. However, the median value of the Type

III cements was lowest. The median value of

the Type I cements was slightly higher, and

the Types II, IV and V had still higher median

values.

The results of the preliminary plots of SB/

S28 versus various individual independent vari23
CD OS OO

do

CO 00 CO rtd

I ^

rtLO OO t^<D

O--" oco

OOCO t-ICO w OOCO

CO O CO

Cvl i-H CO CO

t^CO

CO r- CO (N

I ^

t^OO lot*

1^ CO f-l ^

CO CO coco

cci t^O

loco coco

ICCO oot^ do dd

00 lO Oco dd

coco

COC^

P-CO

coco dd

I ^

CO CCI ICCO

coos

OOCO dd

Ot>

001^

00 iO

CD Tt< dd

I COO CD <N Oco t^-^ ^ I> O i-i coco COtO

I ~"

I ^

o c-x O IM iOCD ^00 c^co

CACi <M00

CO m ^ ic

I I ^

OO

o o OO

dd

lOlO

00 —I OO

o o

o o

lOCD

lOCD

05 ^ OO

OO

Tt* CO

<ji o OOo o OO

COOO (N Tt< OOOOOO

OO OO OO OO

OOOOo o OO

dd

OOOO

OO

dd

I ^

Oi to o^QO(N OO

dd

OO

T-H .-H CO Oi

CO '-^Oi ^ CO ^ lO

0-1 0 C<IO dd dd

^ 00

CO o» »o»o OlO dd

I

CI ^00

CO ^ CO GO OOCO coco cso c^o

OicD cqo

00 t* lO

LO 05 lO OlO CMO OO OO

I ^

I-H CO

CO OO

Tt^iO OOCO

OS CO o IC CO 'rt^tO rtO ^o

OO OO

I ^

005

CO CO

t* lO .-lO dd

I ^

CSIOO Ot^ COCO

OS CO 00 CO .-HO rnO OO OO

I

O CO o o coo '-00

CO lO o »o wo CMO dd dd

I ^ I —

O CO lOlO

00 lO OO

Tj4 OS O W

WCO Tt^ W

CI lO lO 00 CIO CIO OO OO

OO

I ^ OO

OOoco

00 r* OO

I ^

oco t^o

oco OOtIi rH OS coo coo OO OO

OO OO

I ^

T-H CO CO I-* TP d C3S iO

C^si— MO CO CO i-l OO OO

OO OO

cao

CO 00

OS T-< CIOO

lO OS

Tt^os CO CO c o dd

00 r*

CD 00 W OS OClo

to CO CI CI OS Tj< CI lO

00 t* rHO OO OO OO

OO

I ^ OO

I ^

COOO -"i^co cca 00 o OO ""-I

CS i-H CO --I OO OO

OO OO

I ^

TfH 00

COCD CO OO

dd

t^t^ oor*

00 C< I> CO OO OO OO OO

OO OO

OS-^ OOOO

CO o OOCO

ooc:s OO

dd

OSC^ 1^00

CO OS 00 CO -HO O I-H OO OO

OO OO

CO »o t^co OO

o

00

<M

I 05H

m

-A

Tt< t> Ol 00

CM I> --I 00

kO ^ CD O

OO OO

IXO CO

CO o r- O

OO OO OO

(N CD CO O O CD lO (NO O

I> oi>

<MO

II 1! II U II U

(odd)

=

(even)

= U II 11 II

(odd)

=

m m m\ . 02\ . 03\ . ai\ . CO \ . \ . PQ-d pq-o

02 0! 03 10 03 m CQ 10 03 (d 03 m CO lo CO M

MO

+

II 11
Table 9-29. Calculated contributions to the ratio of the shrinkage

of the neat-cement bars at the time of cracking of the annular

specimens to their shrinkage at 7 days, SHBR/SH07 or SB/S7

Inde

v3irifi.blG

Ran^'es of variables percent

Coefficients from eQ 3 table 9-28

Calculated contri- butions to SB/S7

Calculat- ed ranges

of contri- butions to SB/S7

Const. = -1-0.678 C2S** 5 to 50 +0 001.301 + 0 007 to -1-0.069 0.062 CAF 4 to 17 +0.00871 -1-0.035 to -1-0. H8 0.113 MgO 0 to 5 -0.02214 0 to -0.111 0.111 NajO 0 to 0.75 -0.1594 0 to -0.120 0.120 KzO 0 to 1.1 -0.2421 0 to -0.266 0.266 APF *2500 to 5500 -0.0000895 -0.224 to -0.492 0.268 Rb** 0 to 0.01 - 0.403 0 to -0.064 0.064 V** 0 to 0.1 -0.5154 0 to - 0.052 0.052 Ni** 0 to 0.02 -3.418 0 to -0.068 0.068 Cu 0 to 0.05 -1.785 0 to - 0.089 0.089

crnVg.

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

ables are presented in figure 9-5. "Quadrant

sums" with absolute values of 11 or more were

obtained for the independent variables Si02,

ALO,,, FesOs, SO, K2O, C3A, C2S, C4AF, A/F,

S/(A + F), APF, and (air, 1:4 mortar).

Selected equations indicating the relationship

of various independent variables to the ratio

of the nonrestrained shrinkage of the bars at the time of cracking of the annular specimens

to the nonrestrained shrinkage of the bars at 28 days are presented in table 9-31 for the

AE + NAE cements. The use of the percentage

water required for normal consistency in eq 1 did not result in a highly significant reduction

in the S.D. value (see table 9-34). Using com- monly determined variables found to have

coef./s.d. ratios greater than 1 in eqs 2 and 4,

highly significant reductions in the S.D. values

Table 9-30. Frequency distribution of the cements with respect to the ratio of the shrinkage of neat cement bars at the time of cracking

of the annular specimens to their shrinkage at 28 days {SHBR/SH28 or SB/S28)

Shrinkage ratio

0.02 0.06 0.10 0.14 0.18 0.22 0.26 0.30 0..34 0.38 0.42 0.46 0.50 Type cement to to to to to to to to to to to to and Total

0.06 0.10 0.14 0.18 0.22 0.26 0.30 0.34 0.38 0.42 0.46 0.50 over

Number of cements

I 8 15 11 12 11 8 1 5 1 1 73

IA 3 1 3 1 8

11 1 3 7 13 22 7 4 1 58

IIA 1 1 2

III 5 5 3 3 2 1 19 IIIA 1 1 2

IV, V 2 3 2 3 2 2 14

Total ._, 14 27 25 35 37 20 8 8 1 0 0 0 1 176

were obtained, and with the additional use of

the trace elements Rb, Ni, V, and Cu in eqs 3

and 5, further significant reductions in the

S.D. values were obtained. In the equations for

the "odds" and "evens" (eqs 3A, 3B, 5A, and

5B) all of the trace elements as well as CoS had

coef./s.d. ratios less than 1 in one or the other

of the equations calculated with the smaller

groups of cements.

A similar series of equations is presented in

table 9-32 for the NAE cements. The use of

commonly determined variables in eq 2 resulted

in a highly significant reduction in the S.D.

value, and the addition of the trace elements

Rb, Ni, V, and Cu resulted in a further significant reduction in the S.D. value (see table

9-34). Comparing eqs 4 and 5 it may be noted

that the coef./s.d. ratio for CaO was less than

1 when MgO was not used as an independent

variable in equation 4 but was greater than 3

in eq 4 when MgO was used. The use of com- monly determined variables in eqs 4 or 5 re- sulted in highly significant reductions in the

S.D. values and the additional use of the trace

elements in eq 6 resulted in a further significant

reduction in the S.D. value. The eqs calculated

for the "odds" and "evens" in the array of

cements (eqs 3A, 3B, 6A, and 6B) indicated

that C2S, Rb, Ni, and Cu had coef./s.d. ratios

less than 1 in one or the other of the pairs of

equations, and that the coefficient for V had a

change of sign in eqs 3A and 6A.

In tables 9-31 and 9-32 the coefficients for

fineness, KoO, and NaoO were the most highly

significant and an increase in these variables was associated with a decrease in the SB/S28

ratio.

Using the coefficients of eq 3 of table 9-32

and the approximate ranges of values, calculations were made of the contributions and

ranges of contributions of the various independent variables. The results of these calculations are presented in table 9-33. Fineness values

and KoO content of the cements had the greatest calculated ranges of contributions to the

SB/S28 ratios.

25
00 CO oooodoI 2 fl

Oco

00 ;o

r-llO -HO

O <D (M

Tj< 00 <D 00 i-d do I I -

o^COCON

CO (N CO CD

CO T}<

00 Ol

00 Ol

in o CO CO ooI ^ oo

CO 00 CD U3C^ TJHO

COO

lo CD

CO »-' Oi

l^CO I ^ 0(M

COtJI oo

rtd

l.'5'<< OC

O CO 00 CDT- rtO I OOI ^

00 00 oco

l^CO

<N CI

COX o:r^ OOJ — 

00 CO CO

O

CO-* ICCO OO oo ooI ^

00O5 oco

CD O"- ^

00— coo

INI ^

TjH CO 00 CD COCO COOO CO— —CD

CO(M I ^ CO I ^

1-1 CO

rlH CO

C?>00

Tt<

O oooo

OO

COOO noOOooOOoo

OO oo oo oo OO oo oo oo

— ^

>o o oo o oooo

O C3i CO ^

IN ai '-^ CO o ^ — oo oo

oo ooI ^ oo ooI ^ oo ooI ^ ooI ^ ooI ^

lOO wot^(N — o

coo

-^co ox r^'^

CD CO i-t Ttl »0 CO 05 CO — o —o

xt~ — o

IN o<N O

t^r~ oco

^(M lOTji CO CM CO — O (MO ooI ^ oo ooI ^ ooI ^ oo ooI ^

1-1 O) t^co

coc^ r-O

coco oco

CO— o

IN

m CO

Tti CO ^ C-1 coco TjHCO i-iO —o

coo;

1-1 CO IC(N

to CM xco

C^l

—

— Tjl CO o c-1 lii CO CD CO — o —o

ooI ^ oo oo ooI ^ ooI ^ oo ooI ^

coo

XCD

oco oo

CM CO

Tjl to

C-l CO xo oo coo coco

CO c-iirt i-iO ^o oo oo

— o oo

CO C^l

C^J o oo

OiCO O 1-1 CM O ooCDC. OiCO

Tti CO

CM

O oo

ooI ^ ooI ^ ooI ^ ooI ^ oo ooI ^ oo

toco oxin Tti

CM lO 00^ oo oooo COI^ o:X coo

LO CD

O

— o — 

OO oo

oo oo oo

O CO cox

CO

— oo

OCD OOoo

INO m CM OOoo

oo oo

Tjl

O CO CD oooo

IN CM l^O

OCD oo

—

O CO ICX oooo

o>o

CO oo

oo oo oo oo

CM CM CO 1-1 X CO lO 05 CM 'll coo 1*0

cox

1^ CO

CO Tjl

Til o

050

1^ CM CO CD

Tjl

O

CMO ^ lO CO Til OI

C^l CDX 1-1 *o i*co xr^ C5X

— »o

1-1

X Til CO t^CO »OtJI XTfi oo+^U II

P3T3

oo+'-'

II II

paT3

ai in

oo

03 »

oo —o

CQ-O

II II

fO-r

—

O i-iO —o

II II II II II II s o «cc

I- -i; c *

-E2 «

(NCOI OVw

>-) n

<; H

— CO ooX Tji oooo

dd

g..2

—

x cot~

Tjiio col-no a>x — oI ^ ooI ^

Tji CO O ic XX— d

CM CO COCO

to Tjl eocM

CM

—

XcD

CD05

to CM oo ooI ^

COCM OtO X Tji CO CM OtJI oco

—

to CM CDcJi

N 1-H Tji CM I " I "-^

COt^ '^O

CM to CD CO — 1-31 Xto

coo

CO CO CO Tji

Tji CM I ^ CM CO I ^

CM

—

CM •* OlO

OI to CD XX XCM

t^h- t^X dd rtd

lOi-l Xto

CO CO

CM CM

i^lO too

CM— OlTti CM Tfi ox t*-^ lOCM ooI oo

Tji to to-*

CM

—

Oi to—

a> rti CO CM I ^

Xto — X too oooo

XCM toco

Tji

X o —

too CD

— oo oo oo

oooo

CO cnX to o ooo o oo

Xt^

CDtoo oooo

toco —

coo oo

ooI ^ ooI ^ ooI '~' ooI ooI ^ ooI ^ ooI ^ ooI

CD Tjl coo

^- CM — o

t005 o — O CO CD

CO CM Oi CO — o — 

o —

toco

CD CO — o

coo ooO CM CM O

oco O CM

CM

O ooI ^ ooI ^ ooI ^ ooI ^ ooI ^ ooI ^ ooI ^ ooI *o

COCM — o

caco OJCO

05C0 1-ICM CM CM O — O — 

coco ooTji CM — ococo a to

CO CM wo

Xc» — CO to IN — o

toco coco

Tji CM — o ooI ooI ^ ooI 

ooI ^ ooI ^ ooI ^ ooI

CD to

CD

— CO

i^t^ oo O to Oi to

Til CO Tji to — o — 

oo oo

OCD

Ttl CM Ttl — o OO

ooI ^ oo ooI ^ ooI X

—

CMX CM 1^1 CM O oo

coo OI^

t^Tjl CM O oo

to

CM

O oo

OOI ^ ooI ^

XXO TJH oxoco oo

CO to O X to Tjl — o oo

oxoo

CMO oo

oo ooI ooI ^ ooI o to t-^x

CO

— oo

OtJi —CO

CM

X CO CD

to— Til CM o o o o oo oo

Ttl CM

to 1^

Tf CM oooo

oo oo oo

CO CD oo

0103 TJICO — O o: 1-1 O CD X Oi — o oo ootOX

CM

X

— o oo

oo oo oo oo

toCDOl

CO o

Ttl CO OtO

CM Ttl Tl<0 OO

II II OO

II II M CO

CMO lOt^ O Ttl CO CO

Ttl Ttl

X CD

Ttl

O TtlO

dd

Tf

O CM CO Oco f o

Ttl to

to

—

to to

to CM t^o too

toco oo Oo

II II

CQ-D

oo

II II m m

— o

ooI ^

*OJ CMX

CMr^ —CO

WCM cox

lOCM CMi-l

t^— CDtJ^ O to CO

Ttl Tjl to CO

CO CO 1-1 CO

toco C0[>

Ttl

O COCO — to — o o o o o o oo oo

oo

CO

O

—

X to CO CM

w CO

O CO

CMO CM

O oo

CMCO CMX

CO— O05 — Ttl CD CM — o — 

ooI ^

cot^ X to coco

CM

O oo

ooI ^

OOiX

— CD

O Oi I^CD OCD — O CM O oo OO

ooI ^

Ttl

X

O CO CO

CO—

O Tji

—

X CO CD Tli

O Tt* -lO i-tO i-iO +^ u u nil II II

26
Table 9-33. Calculated contributions to the ratio of the shrinkage

of the neat-cement bars att the time of cracking of the annular

specimens to their shrinkage at 28 days, SHBR/SH28 or SB/S28

Inde- pendent

variable

Ranges of variables, percent

Coefficients from eq. 3

table 9-32

Calculated contri- butions to SB/S28

Calculated ranges

of contri- butions to SB/S28

Const. = -1-0.440 C2S** 5 to 50 -1-0.001019 +0.005 to +0.051 0.046 CiAF 4 to 17 +0.00529 +0.021 to +0.090 0.069 MgO 0 to 5 -0.01407 0 to -0.070 0.070 NaiO 0 to 0.75 — 0. 1292 n n no

7

0 097 K2O 0 to 1.1 -0.1695 0 to -0.186 0]l86 APF *2500 to 5500 -0.0000548 -0.137 to -0.301 0.164 Rb** 0 to 0.01 -4.126 0 to -0.041 0.041 Ni** 0 to 0.02 - 2.083 0 to -0.042 0.042 V** 0 to 0.1 -0.3532 0 to -0.035 0.035 Cu 0 to 0.05 -1.141 0 to -0.057 0.057

*om-/g- Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

Table 9-34. "F" values for significance of reduction of variance due to added variables

Table Equations* ..p., ratio D.F.

Critical "F" Ratio

a = 0.01 a = 0.05

9—2 0,

1

10.20 2:161 4.74 3 . 05 o!2 17'.84 7:156 2 . 75 2.07 2,3 3.30 5:151 3 . 14 2 . 27 0,4 17.27 8:155 2.62 2.00 45 3. 12 4:151 3.44 2.44

9-3 0,1 7.59 2:149 4. 75 3.05 0,2 14.98 7:144 2 . 77 2.07

2 3 3 . 54 5:139 3.15 2.27 04 15 . 12 7:144 2.77 2.07

4,5 3^85 6:138 2.94 2. 16

9-6 0,1 2.37 2:163 4.74 3.05

0 2 5.91 4:161 3.43 2.44

2^3 9 99 4:157 3.43 2.44 34 5 loo 3:154 3.90 2.68 05 5 98 5'160 3.13 2.27

5^6 7^45 5!l.55 3. 15 2.27

6,7 5.95 3:152 3.90 2.68

9—7 0 1 1 . 84 2:151 4.75 3.05

0 2 4.41 4:149 3 . 44 2 . 44

2 3 9 84 4.145 3^44 2^44 3^4 4

'.69 4^141 3.44 2.44 0,5 4.64 5:148 3.14 2.27

5,6 7.39 5:143 3.15 2.27

9-10 0,1 0.71 2:163 4.74 3.05

0,2 3.58 5:160 3.14 2.27 2,3 14.33 5:155 3.14 2.27

3,4 5.36 4:151 3.44 2.44 0,5 12.01 8:156 2.62 2.01

5,6 4.08 6:151 3.14 2.27

9-11 0,1 2.80 5:148 3.14 2.27

1,2 23.08 3:145 3.90 2.68

2,3 5.74 5:140 3. 15 2.27 0,4 11.36 8:145 2.63 2.01 4,5 4.95 6:139 2.94 2.16

9-14 0,1 13.58 8:163 2.63 2.01

1,2 12.67 3:160 3.89 2.68

0,3 15.53 7:164 2.75 2.08

3,4 12.86 3:161 3.89 2.68

9-15 0,1 13.22 8:151 2.63 2.01

1,2 13.92 3:148 3.90 2.68

0,3 14.96 7:152 2.76 2.08

3,4 13.95 3:149 3.90 2.68

9-19 0,1 7.09 2:168 4.72 3.05 0,2 25.5 8:162 2.60 2.00

2,3 5.47 4:158 3.43 2.43 0,4 29.0 7:163 2.75 2.07

4,5 7.14 3:160 3.90 2.67

9-20 0,1 6.08 2:156 4.75 3.05 0,2 23.1 8:150 2.63 2.00

2,3 6.27 4:146 3.43 2.44 0,4 26.6 7:151 2.76 2.08

4,5 6.22 4:147 3.44 2.43

Table 9-34. "F" values for significance of reduction of variance due to added variables—Continued

Table Equations* •'F"

ratio D.F.

Critical "F" Ratio

a = 0.01 0 = 0.05

9-23 0,1 2.75 2:167 4 . 74 0 . 05 0,2 19.03 7:162 Z . / 0 2,3 2.82 4:158 3.43 2.44

0,4 18.59 7:162 2.75 2.08

4,5 2.71 3:159 3 . 89 0 AQ £, , 00

9-24 0,

1

2.25 2:155 4 . 75 Q ftK 0 . Uu 0,2 18.95 7:150 2 . 76 2,3 3.18 3:147 3.90 2.68

0,4 18.44 7:150 2.76 2.08

4,5 2..50 3:147 3 . 90 2 . 68

9-27 _ . 0,

1

3.89 2:165 4 . 74 0,2 20.75 9:158 2 . 52 1 . 93

2,3 4.32 4:154 3.44 2.44

0,4 23.77 8:159 2.63 2.01 4,5 4.14 4:155 3 . 44 2 . 44

9-28 - 0,

1

3. 10 2:153 4 . /O 0 . uo 0,2 26.25 7:148 2 . 76 £, . Uo

2,3 4.38 4:144 3.44 2.44

0,4 30.61 6:149 2.94 2.16

4,5 3.47 5:144 3 . 15 2 . 27 9-31.- . 0,

1

3 . 04 2:165 4 . 74 0 . 05 0,2 27.64 7:160 2 . 75 2 . 08

2,3 4.39 4:156 3 . 44 2 . 44 0,4 33.91 6:161 2.92 2.16

4,5 4.23 4:157 3.44 2.44

9-32 0,1 2.52 2:153 4.75 3.05

0 2 27.77 7:148 2.76 2.08

2^3 4!07 4!l44 3.44 2.44

0,4 32.24 5:150 3.15 2.27

0,5 34.09 6:149 2.93 2.16

5,6 4.07 4:145 3.44 2.44

*Equation 0 refers to the variance for the values themselves with no

fitted equation for the AE+ NAE cements.

5.9. Results of Duplicate Determinations

The results of a series of duplicate determinations made on 20 non-air-entraining cements

are presented in table 9-35. The range of val- ues with this group of cements was not so great as was obtained with those of the larger

study. The S.D. values of the duplicate determinations are naturally much smaller than

those obtained for the calculated equations. The

duplicate determinations, though made on different days, did not extend over so long a

period of time as the tests made on the larger

group of cements. If laboratory conditions

varied over the longer time period this may also

have contributed to higher S.D. values.

5.10. Comparative Test-Values on Other Hydraulic Cements

The restrained and nonrestrained shrinkage

tests were also made on two commercial portland-pozzolan cements and seven portlandblast-furnace-slag cements using the same test method previously described with neat cement

pastes of normal consistency. The average time

of cracking of the annular specimens was 11.3

hr with a range of 1.6 to 27.4 hr. The average

shrinkage of the nonrestrained bars at the time

of cracking of the annular specimens was 0.043

percent with a range of 0.016 percent to 0.074

27
Table 9-35. Comparison of estimated standard deviation values of duplicate determinations with those of the calculated^equations

Test Range of values for cements used for duplicate determinations

Estimated

S.D. for duplicate determinations

Estimated

S.D. values

for equations Eq and table

in text

0.047% to 0.082%

0. 126% to 0. 176%

0.185%o to 0.276%o

0..3 hr to 2.33 hr O.dl5%o to 0'.058%, 0.082 to 0.413

0.051 to 0.264

0.002

0.003 0.004

0.87 0.002

0.014 0.009

0.010

0.024

0.029

5.36

o!oo9 0.075

0.049

3;9-3

4;9-7 3;9-ll

3;9-24 3;9-28

3;9-32

Shrinkage (nonrestrained) at time of cracking annular specimens

Shrinkage time of break divided by nonrestrained shrinkage at 7 days

Shrinkage time of break divided by nonrestrained shrinkage at 28 days

* These values were calculated on the time-of-break rather than the square root of the time of break.

percent. The average shrinkage at 28 days was

0.240 percent with a range of 0.174 percent to 0.339 percent. The values for shrinkage of the

nonrestrained bars and time of cracking of the

annular specimens were within the ranges of

the values obtained with the portland cements.

5.11. Comparison with Cements from Other

Sources

Mather [19] has reported values for the nonrestrained shrinkage and time of cracking of

neat cements used in the Portland Cement

Association long-time study of cement performance in concrete [20]. Annular specimens

made of these cements had an average time

of breaking of 13.5 hr with a range of 0.4 to 31.8 hr. The 28-day nonrestrained shrinkage of

these cements averaged 0.207 percent with a range of 0.147 to 0.313 percent. The average

time of breaking of annular specimens made of

these cements was somewhat greater, (13.5 versus 10.4 hr) indicated in this report, and

the percentage shrinkage at 28 days somewhat

lower for these cements, (0.207 versus 0.225)

indicated in this report. The averages and

ranges of values reported for both groups of

cements were in reasonable agreement.

6. Discussion

6.1. Nonrestrained Shrinkage Versus Age

The average values for percentage shrinkage

of the neat portland cement bars of normal

consistency after curing for 24 hr in moist air,

and then exposed to laboratory air were presented in tables 9-2, 9-6, 9-10 and 9-14 for 1, 7, 28 days and 6 months. The average values

for the NAE cements are also presented graphically in figure 9-7. Also presented in this fig- ure are percentage-shrinkage values for six

individual cements at 1 hr to 1 year (on a log

scale) to indicate the approximate range of

values obtained. (Using the log scale for time

resulted in the concavity of these curves.) Approximately 85 percent of the 1-year shrinkage

had occurred at 28 days and there appeared to be very little shrinkage of most of the specimens after 6 months. The annular specimens of

the three cements represented by the upper

three curves (labeled 1, 2, and 3) cracked at

0.1, 0.6, and 1.1 hr, whereas those represented

by the lower three curves (labeled 4, 5, and 6)

cracked at 22, 14, and 17 hr respectively.

It is generally recognized that variations of

CO2 content in the laboratory air may have

been a contributing factor to the shrinkage

values which were obtained. However, the

specimens were all made in one laboratory during a period of about 3 months, and carbonation may be expected to affect all specimens by

about the same amount and would not have affected the relative values obtained.

6.2. Trends of Variables

Single equations from each of the tables re- lating the variables associated with values ob- i tained for shrinkage at the various ages,

shrinkage ratios of the prisms, and time of

cracking of the annular specimens, all made of

NAE cements, are presented in table 9-36. The

equations are presented vertically instead of

horizontally, and the coef./s.d. ratios, and cal- culated ranges of contributions of the independent variables are presented as in previous

sections.

It may be noted in table 9-36 that an increase

in the C3A was probably associated with a de- crease in SHBR but the effect was of minor

importance. An increase in C3A was associated

with lower shrinkage at 1, 7, and 28 days when

used with C3A/SO3 and SO3 as well as other

additional variables. An increase in the C3A

content is normally associated with greater

| shrinkage but, as indicated by Lerch [14] and I Picket [15], the shrinkage of mortars and concretes made of high C3A cements may be substantially reduced by use of an optimum gypsum content. The interaction of the three

independent variables C3A, C3A/SO3 and SO3

in the equations may have accounted for the

negative sign for the C3A coefficient. The effect

of differences in C3A, C3A/SO3, and SO3 on

shrinkage of the neat bars was relatively great.

It may be noted that for the neat cement bars,

moist cured for 24 hr, an increase in the C3A/

28
1 HR. 3 HR. 6 HR. 24 HR. 6 DAY 27 DAY 6 MO. I YR. TIME OF SHRINKAGE Figure 9-7. Results of plotting the average percentage shrinkage of neat

Portland cement pastes of normal consistency cured for 2h hours in moist air and then exposed to laboratory air for periods up to 6 months.

Also presented are the percentage-shrinkage values of six individual cements (labeled

1, 2, 3, 4, 5, and 6) versus time, selected to show the range of values obtained.

SO3 ratio and an increase in SO3 were both

associated with greater shrinkage, the C3A/

SO3 at 1, 7, 28 days and 6 months, and the SO3

at 1 and 7 days.

The samples of the cements used for these

shrinkage tests were obtained at a time when

the upper limits of SO3 were lower than they

are in present specifications. It is therefore

probable that the amounts of SO3 were below

the optimum values for most, if not all, of the

cements. It would, therefore, be of questionable

value to use the coefficients of SO3, C3A/SO3,

and C3A with the SO3 values permitted in present specifications. Neither C3A, C3A/SO3 nor SO3 had coef./s.d. ratios greater than 1 in the

equations for the time of cracking of the annular specimens or the shrinkage ratios, SB/S7

or SB/S28. The effect of C3A and SO3 as well

as other independent variables associated with

the shrinkage of concrete specimens will be discussed in the next section of this series of

articles (see page 37)

.

In table 9-36 it may be noted that an in- crease in the C4AF may be associated with a

decrease in shrinkage at 24 hr, and possibly

with an increase in the shrinkage ratios SB/S7

and SB/S28. An increase in C4AF also appeared to be associated with an increase in the

time of cracking of the annular specimens.

Differences in the C3S and CoS contents of

the cements were not significantly related to the shrinkage values or ratios obtained for the

different cements. An increase in C2S may possibly be associated with a longer time period

for the restrained annular specimens to break.

Higher MgO values appear associated with

lower SHBR values and lower shrinkage ratios

but possibly with greater shrinkage of the neat

cement bars at 28 days and 6 months.

29
Table 9-36. Coefficients, coef./s. d. ratios, and caladated ranges of contributions of independent variables associated with nonrestrained shrinkage at various ages of neat cement bars of normal consistency, time of break of annular specimens, and shrinkage ratios for NAE cements

Equation 3 3 4 3 2 3 3 3

9-24 9-3 9-7 9-11 9-15 9-20 9-28 9-32

DcpcndcDt Variable — - SHBR

+0. 101 — 0 nnnfi? 2 .

0.001

SH24

-0.020 — 0.00553

3.2 o'o83 — 0.00137

3.0 0.018

SH07

-0.032 — 0.0165

4.4 0^248 **_0. 00192

l!9 o!o25

SH28

-0.023 — 0.0204

0^306 **_0. 00217

1.7 0!028

SH6M

+0.004

-0.0060

2.3 0.090

(TOBR) »-5 +6.24

SB/S7 +0.678

SB/S28 +0.440

+0.1455

4.8

1.89

+0.0087

3.1 0.113

+0.0053

2.9 0.069

Cr\o( /a H

nf\af ** +0.00067

1.2 0.027

Prtof /q H

+0.0307

2.9

1.39

**_0.0014

1.6 0.062

**^-0. 00102

1.7 o!o46

Cne^f /a r1

+0.0101

3^4 o!o98 +0.0351

4.4 0.084

+0.0281

4^3 0.273 +0.0722

4.2 0.174

+0.0368

4.2

0.357 +0.0788

2.5 0.188 + 0.0054

2.4 0.044 +0.0921 6.0

0.069 +0.0779

o'o86 +0.0000133

2.3

0 . 040

+0.0175

3.5 0.170

SOa, coef **-0.266

1.1 0.64 -0.1475

2.4 0.73 -1.54

3.8

1.15 — 2.27

5!7 2.50 -0.001002

6.0 3.07

Coef./s.d Calculated range MgO, coef -0.00202

3.0 0.010 -0.0150

3.3 0.011 — 0 0999 5.0 0.025 -0.0000124

8.0 0.043

+0.00879 2.8

0.044 +0.1392

6.9 0.104 +0. 1233 6!o

o! 135 +0.0000224

2.7 o'o67

-0.0221

4.1 0.111 -0.1594

4.4

0.120 — 0.2421

6^7 0^266 — 0.000090

0.268

-0.0141

3.9 0.070 -0.1292

5.5 0.097 — 0. 1695

7! 1 0! 186 — 0.0000548

6^7

0. 164

Coef./s.d Calculated range Na20, coef Coef./B.d Calculated range

Hnpf /r h

APF prjpf Cnpf /« d

1 '4 mortaF coGf

**+0.0100

1.9 0.008 +0.0200

4 .

0. 022 +0.0000046

2*3 o!oi3

+0.3133

2.5 0.023 +0.0383

3.5 0.042 +0 . 0000088

2!o o'o26 **+0. 00144

1.2

I Pill o tori fQ rnYo 0.029 +0.0041

2.7 0.010

+0.544

4! 1 1.80 — 8.94

1 . 79

Pnpf /ft H

I^H loil 1 Q + Oft T'nTKTO

**-|-0.0523 1^6 0.010 +0. 4422

2.

o!oo9

+0. 1828 2.7 o'o37 +0.3194

3*4 o]064

+0. 575 5.0

o! 115 Cnpf A H

Coef /s d

Cu coef — 0.2483

2.4 o!oi2

— 1 . 785

2.1 o!o89 **-3.418

1.6 0.068

— 1.141 2.0 o!o57 **-2.083

1.4 0.042

Oopf /s H Oalculatsd ran^c + 2.617

2.2 0.052Coef./s.d

P coef **-|-0.0130

1 .

o'o06

**+0.0262

1 .

o!oi3 +2.667

2.4

0 . 027

+0.0489

2.3 0.024 + 3 . 02

2!l 0.030

Pnpf /ft H

flsi Ipil I O +.pn T"Q rt oro

Pnpf H Cq 1 Pn 1 Q f oH TQ n nro

**_ 0.6045

1*3 0.060 **_ 0.0555

1 .

o!oo6

1 .

0.037

— 96.5

2 .

0. 96

**_(5,403

1 .

0.064

0.515

1 4 o!o52

**_4, ]26

1

.*7 0.041

1 4 o!o35

^^Ucl,/ tS.Cl dilfiilotoH fnnofO **- 0.0323

1.1 0.006

**- 0.0964

Coef./8.d 1.1 Calculated range 0.019 **-2.89

1.7 1.44

Coef./a.d

* The calculated range was computed from the range of values for the cements times the coefficient for each independent variable. ** The independent variable is probably not significant as the coef./s.d. ratio is less than 2.

30
The results reported in table 9-36 confirm

previously reported information that alkalies are associated with shrinkage. An increase in

Na20 was associated with lower nonrestrainedshrinkage values at the time of cracking of the

restrained-shrinkage annular specimen, as well

as the shorter period of time of cracking of the

annular specimens. An increase in NaoO was

also associated with higher shrinkage values at 28 days and 6 months and possibly also at 7

days.

An increase in K2O was also associated with

lower SHBR values and lower TOBR values

and with higher shrinkage at all ages of 1 day

to 6 months. Differences in K2O values and fine- ness of the cements appear to be the major

factors causing early cracking of the annular

specimens made of neat cements.

An increase in the fineness also appears asso- ciated with lower nonrestrained shrinkage val- ues of the bars at the time of cracking of the

annular specimens as well as the shrinkage

ratios. Increases in fineness may possibly be

associated with greater shrinkage values at ages 1 day to 6 months, but the coef./s.d. ratios

obtained were significant only at the 5-percent

probability level. An increase in the loss on ignition may be

associated with an increase in the time re- quired for the annular specimens to crack, and

an increase in the nonrestrained shrinkage of

the bars at the time of cracking of the annular

specimens.

Of the various trace elements in the cements,

only Ba appeared highly significant in its re- lationship to values obtained in any of the

tests. An increase in Ba appeared associated

with an increase in shrinkage values at 28 days

and 6 months and probably at 7 days. Increases

in Ba are probably also associated with a

shorter period of time for cracking of the

annular specimens. Of the other trace elements,

increases in Cr may be associated with in- creased 24-hr shrinkage, increases in Cu with

decrease in nonrestrained shrinkage at the time

of cracking of the annular specimens, increases

in Ni with increases in 6-month shrinkage of

the bars, increased P with increased 28-day

shrinkage and increased Rb with increased 7- and 28-day nonrestrained shrinkage.

6.3. Shrinkage Characteristics of Neat Cement

Pastes Versus Compressive Strength of

1:2.75 (Cement to Sand) Mortars

Two reports by A. de Sousa Coutinho [16,

17] indicated that with neat cement pastes, a

greater cracking tendency was associated with

higher strength and that the reverse was true

with concretes. The findings by A. S. Coutinho

may have contributed to the withdrawal of the

proposed neat-cement restrained-shrinkage test from the RILEM specifications. No strength

tests, either tensile or compressive, were made

on the neat cement pastes used for the nonrestrained shrinkage tests or the time of cracking of the annular specimens. It therefore appeared desirable to determine the relationship

of shrinkage values, ratios, and the time of

cracking to the available compressive-strength

data of the 1 : 2.75 (cement to graded Ottawa

sand) mortars. These equations for the NAE

cements are presented in table 9-37. Also presented are the reduction in variance or "F"

values resulting from the calculation of a constant and the coefficient of an independent variable. An "F" value greater than 3.05 is significant at the 5-percent probability level and, if greater than 4.7, at the 1-percent probability

level. It may be noted in table 9-37 that an

increase in compressive-strength values of the

mortar at 1, 3 and 7 days, (eqs 1, 2, and 3) was

associated with the 24-hr shrinkage of the neat

cement bars. Higher compressive-strength val- ues of the mortars at 1 year were associated

with lower shrinkage values for the neat ce- ment bars at 7 and 28 days and at 6 months

(eqs 10, 15 and 20). (The compressive-strength

values of the 2-in cubes were all determined

with moist specimens that had not been subjected to any drying cycles).

Higher compressive-strength values for the

mortars at 1, 3, 7 and 28 days appeared associated with lower values of nonrestrained

shrinkage of the neat cement bars at the time

of cracking of the annular specimens, (eqs 21,

22, 23, and 24) as well as a shorter time for

the annular specimens to crack, (eqs 26, 27,

and 28). Equations 25 and 30 indicate that

higher strength values for the mortars at 1 year may possibly be associated with higher

nonrestrained shrinkage of the neat cements at the time of cracking of the annular specimens

and a greater time before the annular specimens cracked. Equations 31 through 40, relating the nonrestrained-shrinkage ratios of the

neat cements to the compressive strengths of

the mortars, also indicate the reversal of the

sign of the coefficient for the 1-year compressive-strength relationship.

The relationships in table 9-37 indicate that

variables associated with the shrinkage tests of

the neat cement pastes may also be associated

with the compressive strengths. Referring to section 7 of this series and table 7-77 of section

7 [11] it was noted that, although higher val- ues for fineness and C3A were associated with

higher compressive strengths at the early ages,

higher values for C3A were associated with

lower strength at 1 year (STIY). Differences

in fineness and C3A values were of major significance in the equations for strength of the

mortars at 1 and 3 days but not in the equations

for shrinkage of the neat cements at 24 hr. A

comparison of the effect of the alkalies NaoO

and K2O in tables 7-77 and 9-36 are also of

31
Table 9-37. Relationship between shrinkage, shrinkage ratios, and time of cracking of neat portland cement pastes, and the compressive

strength in psi of 1:2.75 {cement to sand) mortars at different ages

Equation Note

(2)

(')

Dependent

variables

Independent variables

Const. SH24 +0.0541

s.d. (0.0036) SH24 +0.0476

s.d. (0.0044) SH24 +0.0466

s.d. (0.0052) SH24 — +0.0571

s.d. — (0.0089) SH24 — +0.0897

s.d. — (0.1117) SHOT — +0.1414

s.d. (0.0075) SH07 +0.1338

s.d. (0.0093) SH07 +0.1323

s.d. (0.0108) SH07 +0.1609

s.d. — (0.0179) SH07 +0.2174

s.d. (0.0233) SH28 = +0.2200

s.d. (0.0102) SH28 +0.2094

s.d. — (0.0128) SH28 +0.2058

s.d. (0.0148) SH28 = +0.2424

s.d. (0.0245) SH28 +0.3537

s.d. (0.0311) SH6M +0.2681

s.d. = (0.0125) SH6M +0.2587

s.d. = (0.0156) SH6M = +0.2560

s.d. (0.0181) SH6M +0.2970

s.d. = (0.0298) SH6M = +0.4340

s.d. (0.0378) SHBR +0.0484

s.d. = (0.0023) SHBR — +0.0505

s.d. (0.0029) SHRB = +0.0530

s.d. (0.0034) SHBR + 0.0527

s.d. = (0.0060) SHBR + 0.0143

s.d. (0.0082) TOBR — + 17.81

s.d. = (1.38) TOBR +20.25

s.d. (1.69) TOBR +22.38

s.d. (1.98) TOBR +22.78

s.d. - (3.57) TOBR -2.78

s.d. (4.88) SB/S7 +0.3593

s.d. (0.0208) SB/S7 — +0.3793

s.d. (0.0261) SB/S7 — + 0.4048

s.d. — (0.0306) SB/S7 = +0.3680

s.d. (0.0547) SB/S7 +0.0128

s.d. (0.0721) SB/S28 +0.2363

s.d. (0.0139) SB/S28 +0.2493

s.d. (0.0174) SB/S28 +0.2661

s.d. (0.0204) SB/S28 +0.2453

s.d. (0.0364) SB/S28 -0.0095

s.d. (0.0476)

STOl ST03 ST07 ST28 STIY +0.0000121

(0.0000034) 0.0178 6.4 +0.0000084

(0.0000019) 0.0175 9.4 +0.0000058

(0.0000015) 0.0177 7.4 +0.00000172

(0.00000171) 0.0184 0.5 -0.0000038

(0.0000018) 0.0182 2.1 +0.0000089

(0.0000070) 0.0370 0.8 +0.0000075

(0.0000041) 0.0368 1.6 +0.0000054

(0.0000032) 0.0369 1.4 *- 0.0000021

(0.0000034) 0.0372 0.2 -0.0000107

(0.0000037) 0.0363 4.2

* + 0.0000072

(0.0000097) 0.0508 0.3 +0.0000081

(0.0000056) 0.0505 1.1 +0.0000064

(0.0000043) 0.0505 1.1 *- 0.0000030

(0.0000047) 0.0508 0.2 -0.0000201

(0.0000049) 0.0484 8.4 *+ 0.0000082

(0.0000118) 0.0619 0.2 +0.0000080

(0.0000068) 0.0617 0.7 +0.0000061 _(0.0000053) 0.0617 0.6 *- 0.0000041

(0.0000057) 0.0619 0.2 -0.0000250

(0.0000059) 0.058S 8.9 -0.0000134

(0.0000021) 0.0114 19.8 -0.0000070

(0.0000012) 0.0116 15.6 -0.00000534

(0.00000099) 0.0117 14.7 -0.00000340

(0.00000116) 0.0124 4.3 +0.00000331

(0.00000128) 0.0125 3.3 -0.00769

(0.00129) 6.86 17.8 -0.00456

(0.00073) 6.80 19.4 -0.00364

(0.00057) 6.77 20.28 -0.00243

(0.00069) 7.31 6.30 +0.00206

(0.00077) 7.42 3.64 -0.000110

(0.000020) 0.1037 15.9 -0.000058

(0.000011) 0.1051 13.4 -0.0000461

(0.0000089) 0.1051 13.5 -0.0000227

(0.0000105) 0.1121 2.3 +0.0000378

(0.0000113)

0. 1099 5.6 -0.0000724

(0.0000130) 0.0691 15.5 -0.0000383

(0.0000075) 0.0701 13.0

-0.0000.303

(0.0000059) 0.0700 13.1 -0.0000155

(0.0000070) 0.0745 2.5 +0.0000277

(0.0000075) 0.0725 6.8

* Coef./s.d. ratio less than 1.

' 160 cements, Avg = 0.0658, S. D. = 0.0184

2

•' = 0.1501, ' = 0.0371

8 " = 0.2670, " = 0.0507

« " = 0.2761, " = 0.0618

' 159 cements, Avg = 0.0353, S. D. = 0.01267

6 " = 10.28, " = 7.54

7 " = 0.2515, '• = 0.1134

8 " = 0.1654, " = 0.0754

32
interest. Differences in NaoO were not associated with early strength in equations in table

7-77 but K2O was. In equations of table 9-36

differences in KoO content was of major significance in the time of cracking of the annular

specimens. Increases in both NaoO and K2O

were associated with decreases in the nonrestrained shrinkage at the time of cracking of

the annular specimens.

The literature on shrinkage and cracking of

Portland cement pastes, mortars and concretes

has indicated that many variables are involved,

i Among these are the size and shape of the

specimens, the amount of hydration product,

I the gel-space ratios [21], the moisture gradient

I within a specimen, the moisture diffusivity, the

ability of the structural units in the hydration

products to adjust to the stresses produced by

shrinkage called "creep" or semi-plastic flow,

and the amount of restraint offered by unhydrated cement particles in the cement paste, or

the aggregates in the mortars or concretes. The neat cement pastes of normal consistency, with a water-cement ratio of about 0.25,

hydrated for only 24 hr, may be expected to have a considerable amount of unhydrated ce- ment, and the unhydrated particles would be

closely adjacent to each other. This would result in a considerable restraint to shrinkage in

the paste, or at least more so than in concrete

where the water-cement ratio may be more

than twice as great. Shrinkage tests made on

concrete are usually made after a longer curing

period and under these conditions, the amount

and the nature of the hydration product may

also differ from that at 24 hr.

7. Summary and Conclusions

(1) Determinations were made of the drying-shrinkage of 1 X 1 X 10-in (effective gage

length) bars made of neat cement pastes. The

specimens made of 183 cements were stored

for 24 hr in moist air and then exposed to laboratory air at 50 percent relative humidity.

Tests were also made of the time of cracking

of annular specimens made of the same pastes

and restrained from shrinking by a steel disc.

I The storage conditions were the same as for

the bars. Multivariable regression equations

j were used to determine which of the independent variables or combinations of variables,

, such as fineness and composition of the cei ments, as well as trace elements in the cements were associated to a significant degree with the

il test-values obtained. The test values used as

i dependent variables were the percentage

1 shrinkage at 1, 7, 28 days, and 6 months, the

percentage shrinkage of the bars at the time

of cracking of the annular specimens, and the

time of cracking of the annular specimens rej strained from shrinking. Also used as depen-

: dent variables were the ratios of the nonreijj strained shrinkage at the time of cracking of

I the annular specimens to the nonrestrained

j shrinkage at 7 and 28 days.

I (2) The frequency distributions of the ce- ments with respect to percentage shrinkage at

1, 7, 28 days, and 6 months indicated a wide

distribution of values especially for the Type I

I cements. There was an overlapping of the percentage-shrinkage values of the cements in the

various types as classified. It is then not possible to say that a cement, because it conforms

with the chemical composition and physical re- quirements of any one type of cement, will

therefore have greater or less shrinkage than a cement meeting requirements for some other

type.

(3) The time of cracking of the annular

specimens ranged from 0.1 hr to more than 40

hr after being removed from moist storage and

placed in laboratory air. The average time of

cracking was about 10 hr. Eighty-five percent

of the Types III and IIIA, 59 percent of the

Types I and lA, 41 percent of the Types II and

IIA, and 7 percent of the Types IV and V

cracked in less than 10 hr. The cements classified as Type I had the greatest range of values,

but there was a great deal of overlapping of

the values obtained for the cements of the different types.

(4) The percentage shrinkage of the bars

at the time of cracking of the annular specimens ranged from about 0.010 percent to more

than 0.065 percent with an average of about

0.035 percent. About 76 percent of the Types

III and IIIA, 43 percent of the Types I and lA,

27 percent of the Types II and IIA, and 14 percent of the Types IV and V had shrinkage val- ues less than the average. This indicates, to some extent, the overlapping of values obtained with the different types of cement.

(5) The ratios of the percentage shrinkage

of the neat cement bars at the time of cracking

of the annular specimens to the shrinkage at 7 or 28 days were calculated as possible indications of plastic deformation or creep of the

hydrated pastes. A considerable range of val- ues was obtained, with overlapping of the val- ues for the cements of the different types. The

majority of the Types III and I cements had

values below the average which was not the

case with the Types II, IV, and V cements.

(6) An increase in the percentage water re- quired for normal consistency of the neat ce- ment pastes was associated with an increase in

the shrinkage at 24 hr, but not at later ages.

An increase in the percentage water required

for normal consistency of the neat cement

33
pastes was also associated with a decrease in

the time of cracking of the annular specimens.

(7) Multivariable regression equations were

calculated to determine which of the available

independent variables were associated with the

various determined shrinkage values or characteristics. Typical equations were compiled in

table 9-36

(7.1) Higher C3A/SO3 ratios were associated

with higher shrinkage values at 1, 7, 28 days,

and 6 months when used together with C3A

and SO3 as independent variables. Under these

conditions, higher SO3 values were also associated with higher shrinkage, but higher C3A

values were associated with lower shrinkage

values. Differences in values of these independent variables showed the greatest association

with differences in shrinkage values at 1, 7, and 28 days for all of the variables studied.

None of these independent variables or combinations were significantly associated with the

time of cracking of the annular specimens nor

the shrinkage ratios.

(7.2) An increase in C4AF was associated

with a decrease in shrinkage at 24 hr and an

increase in the time required for the annular

specimens to crack.

(7.3) Differences in C3S and C2S of the ce- ments were apparently not associated with the

shrinkage values obtained. An increase in C2S

is probably associated with an increase in the

time required for the annular specimens to crack.

(7.4) An increase in MgO may possibly be

associated with an increase in shrinkage at 7

and 28 days and with a decrease in shrinkage

of the bars at the time of cracking of the an- nular specimens.

(7.5) An increase in Na20 was associated

with an increase in shrinkage at 28 days and 6

months and a decrease in the time of cracking

of the annular specimens and the nonrestrained

shrinkage when the annular specimens cracked.

(7.6) An increase in K2O was associated

with an increase in shrinkage at all ages and

with a decrease in the time of cracking of the

annular specimens, and with a decrease of the

nonrestrained shrinkage at the time of cracking of the annular specimens.

(7.7) An increase in the fineness of the ce- ments was associated with a decrease in the

nonrestrained shrinkage at the time of cracking of the annular specimens and with a de- crease in the time required for the annular

specimens to crack and possibly with an in- crease in shrinkage at all ages.

(7.8) An increase in the loss-on-ignition val- ues was possibly associated with an increase in

the time of cracking of the annular specimens

Remarks about relations with time of break of annular speci- mens are based on the square root of time of break. See footnote

10, subsection 5.5.

and an increase in the nonrestrained shrinkage

at the time of cracking.

(7.9) The use of trace elements found to have a coef./s.d. ratio greater than 1 in the

equations resulted, in most instances, in a re- duction in variance significant at the 1-percent

probability level. Except for Ba, (and Na20

and K2O, as previously mentioned), none of the

individual trace elements were associated with

the shrinkage characteristics to a highly significant degree. An increase in Ba is probably

associated with an increase in shrinkage at 28

days and 6 months and possibly at 7 days. In- creases in Ba and Rb are possibly associated

with a decrease in the time required for the

annular specimens to crack. Cr, Cu, Ni, P, and

Rb may possibly be associated with shrinking

at one or more ages.

(8) The use of the major oxides instead of

the calculated potential compound-composition

values of the cements (and also using the

AI2O3/SO3 ratios) resulted in equations with

approximately the same reduction in variance

as when the compound-composition values were

used.

(9) Equations computed for all cements,

i.e., the air-entraining cements together with

the non-air-entraining cements, resulted in coefficients and coef./s.d. ratios of the independent variables in reasonable accord with those

obtained when only the non-air-entraining ce- ments were used.

(10) An increase in compressive strength

of the 1 : 2.75 (cement to Ottawa sand) mortars

at 1 day was associated with an increase in

shrinkage values at 24 hr of the bars made of

neat cement paste of normal consistency. An

increase in compressive-strength values of

these mortars at early ages was associated with

a decrease in the time required for the annular specimens to crack and a decrease in

nonrestrained shrinkage at the time of cracking of the annular specimens. An increase in

the compressive-strength values of these mortars at 1 year was associated with an increase

in the nonrestrained shrinkage of the neat ce- ment bars at 7, 28 days, and 6 months.

(11) The estimated standard deviations of

results of duplicate determinations made on

different days were much lower than those

computed from the equations using available

independent variables. It therefore appears

that other independent variables or combinations of independent variables may contribute

to the shrinkage characteristics of hydrated

neat portland pastes.

(12) The averages and ranges of values for

28-day shrinkage, and time of breaking with

restrained shrinkage, of the cements used in

this investigation were in reasonable agreement with those reported for the PCA longtime study of cement performance in concrete.

34
In addition to the acknowledgements indicated in previous sections of this series of

articles, special acknowledgements are made to M. R. DeFore and A. C. Figlia, who conducted

most of the tests, and to Paul Worksman for

studies of the reproducibility of the shrinkage

values and characteristics.

8. References

[1] Symposium on the Chemistry of Cements, Stock- holm, 1938, (Ingeniorsvetenskapsakademien,

Stockholm 1939).

[2] Proceedings of the Third International Symposium

on the Chemistry of Cement, London 1952, Ce- ment and Concrete Association, London.

[3] Chemistry of Cement, Proceedings of the Fourth

International Symposium, Mono. 43, Vol. 1, 2, Aug. 1962, U.S. Government Printing Office, Washington, D.C.

[4] International Method of Cement Testing, Bulletin De La Reunion des Laboratoires D'Essais et De

Recherches Sur Les Materiaux et Les Constructions. RILEM Bulletin No. 12, Dec. 1952, 12 Rue

Brancion, Paris.

[5] Blaine, R. L., Arni, H. T., and Foster, B. E., NBS

Building Science Series No. 2, Interrelations between Cement and Concrete Properties, Part I, Section 1, Materials and techniques (1965).

[6] Blaine, R. L., Arni, H. T., and Clevenger, R. A.,

ibid., Section 2, Water requirements of portland

cement.

[7] Blaine, R. L., Bean, Leonard, and Hubbard, Eliza- beth K., ibid., Section 3, Occurrence of minor

and trace elements in portland cement.

[8] Blaine, R. L., Arni, H. T., and Evans, D. N., NBS

Building Science Series No. 5. Interrelations between Cement and Concrete Properties, Part 2, Section 4, Variables associated with expansion in the potential sulfate expansion test (1966).

[9] Blaine, R. L., and Arni, H. T., ibid., Section 5, Heat of hydration of portland cements.

[10] Blaine, R. L., and Arni, H. T., ibid.. Section 6, Variables associated with small autoclave ex- pansion values of portland cements.

[11] Blaine, R. L., Arni, H. T., and DeFore, M. R., NBS

Building Science Series No. 8, Interrelations between Cement and Concrete Properties, Part 3, Section 7, Compressive strength of test mortars

(1968).

[12] Blaine, R. L., Arni, H. T., and DeFore, M. R., ibid.. Section 8, Compressive strength of steam cured

Portland cement mortars.

[13] Standard Methods for Mechanical Mixing of Hydraulic Cement Pastes and Mortars of Plastic Consistency. ASTM Designation C305-65.

ASTM Book of Standards, Part 9, June 1966,

p. 313. [14] Lerch, William, Proceedings ASTM, 46, 1252

(1946).

[15] Pickett, Gerald, Journal ACI, 19, No. 2, 149 (1947).

[16] Coutinho, A. de Sousa, Lab. Nac. Eng. Civil Pub.

No. 57, (1954) (in Portuguese).

[17] Coutinho, A. de Sousa, Materiaux et Constructions,

Recherches et Essais, RILEM Bulletin No. 5, Dec. 1959, p. 26. [18] Natrella, M. G., Experimental Statistics, NBS

Handbook 91, ch 20 (1963).

[19] Mather, B., Cement Performance in Concrete,

Technical Report No. 6-787, U.S. Army Engineer Waterways Experiment Station, Corps of Engineers, Vicksburg, Miss., Sept. 1967.

[20] Portland Cement Association Research and Devel- opment Laboratories, Bulletins 26, 30, 32, 38, 43,

60, 89, 102, 114 by various authors.

[21] Powers, T. C, and Brownyard, T. L., Bulletin 20, Research Laboratories of the Portland Cement

Association (1948).

35
I
Section 10. Shrinkage and Expansion of Concrete

R. L. Blaine and H. T. Arni

The relationship between the cement characteristics and the drying shrinkages of concretes made of a large number of cements of different types and compositions, as well as the subsequent expansions when the concretes were rewetted, were studied by fitting

multivariable regression equations with the aid of a digital computer. Specimens

6x8x16 inches, were made using 5.5 bags of cement (nominal) per cubic yard with a water/cement ratio of 0.635, as well as with a slump of 5 ± 1 inches. Increases in C3A,

C4AF, fineness of the cement, and air content of the concrete were associated with in- creases in both shrinkage on drying and expansion on rewetting of the concretes. In- creases in Na20, SO3, and ignition loss of the cements were associated with decreases in the shrinkage values of the concretes. None of the individual trace elements, except

possibly Rb and SrO, were associated to a highly significant degree with shrinkage or expansion characteristics of the concretes. The use of trace elements in equations with

other more commonly determined variables resulted in a significant reduction in variance. There was no relationship between the shrinkage of concrete specimens moist cured 14 days and then dried in laboratory air for eight weeks, and the shrinkage of neat cements,

moist cured only 24 hours and then dried in laboratory air. Higher values for dynamic

Young's modulus of elasticity of the concretes were associated with lower shrinkage and

expansion values. Key Words : Cement composition ; expansion-shrinkage ratios ; portland cement concrete; shrinkage of concrete; trace elements. CONTENTS

Page

1. Introduction 37

2. Materials 38

2.1. Cements 38

3. Methods of test 38

3.1. Preparation of concretes 38

3.2. Test specimens 38

3.3. Storage of specimens 39

3.4. Shrinkage and expansion measurements 39

3.5. Weight loss and gain 40

4. Abbreviations 40

5. Statistical analyses 40

6. Results of tests 41

6.1. Cement content of concretes 41

6.2. Drying shrinkage of concretes 42

a. Drying shrinkage of series 0 concretes having a water/cement ratio of 0.635 (OSHR). 42

b. Drying shrinkage of series A concretes having a 5 ± 1 in. slump (ASHR) 43

6.3. Expansion of concretes as a result of rewetting 47

a. Expansion of series 0 concretes made with

a water/cement ratio of 0.635, air dried,

and then rewetted (OEXP) 47

b. Expansion of series A concretes made with

a slump of 5 ± 1 in., air-dried and then

rewetted (AEXP) 50

6.4. Residual shrinkage or difference between the percentage shrinkage during drying and the percentage expansion with subsequent re- wetting 51

a. Residual shrinkage of series O concretes made with a water/cement ratio of 0.635 (ODSX) 51

b. Residual shrinkage of series A concretes made having a slump of 5 ± 1 in. (ADSX). 54

6.5. Ratio of percentage expansion divided by the percentage shrinkage 57

a. Ratio of expansion divided by the shrink- age of series 0 concretes made with a water/cement ratio of 0.635 (OREX = OEXP/OSHR) 57

b. Ratio of expansion divided by the shrink- age of concretes made having a slump of 5 ± in. (AREX=AEXP/ASHR) 57

6.6. The ratio of the residual shrinkage after re- wetting to the initial shrinkage (OREX

andAREX) 61

6.7. Shrinkage of tops and bottoms of concrete specimens as cast 64

7. Discussion 67

7.1. Comparison of equations for the dependent

variables 67

7.2. The effect of trace elements 69

7.3. Agreement of duplicate determinations of per- centage shrinkage and percentage expansion 71

7.4. Shrinkage and expansion of concrete versus shrinkage characteristics of neat cement 75

7.5. Shrinkage and expansion of concrete versus the dynamic Young's modulus of elasticity. 75

7.6. Top and bottom shrinkage and expansion

7.7. Comparative test values on other hydraulic cements 76

8. Summary and conclusions 76

9. References 77

1. Introduction

As indicated in the previous section of this

series of articles, there have been a great number of studies and articles published relative to the drying shrinkage of cement and concrete.

L'Hermite [1] ^ has listed many of these, and

has presented not only an excellent summary,

1 Figures in brackets refer to literature references at the end

of this section, p. 77.

37
but also theories on the relationships of the

various types of volume change. There are many recognized variables that affect the drying shrinkage of concrete, including the water/

cement ratio and the kind of aggregates used, as well as the amount of curing or hydration of

the cement prior to exposure of specimens to drying. Other variables may include the size

and shape of the test specimens as well as the

temperature and humidity at which they are

dried.

L'Hermite has indicated [1] that different

types of hydraulic cements may have quite different shrinkage characteristics, and that the

influence of chemical composition of cement

clinker on shrinkage and creep has not yet been

studied. Swayze has indicated [2] that the ef- fect of the type of cement on ultimate shrinkage of concrete is insignificant, but he did find

considerable differences in shrinkage with both

neat cements and mortars. The relationship, or

lack of relationship, between the shrinkage of

neat cement and the shrinkage of concrete has

long been a matter of controversy. The differing observations of L'Hermite and Swayze appeared to justify a further study of this phe- nomenon. The previous section dealt with the

variables which were associated with the

shrinkage of neat cement paste; this section

deals with the shrinkage of the concretes made

with the same 199 portland cements.

Portland cement concretes that have been

dried expand when rewetted but the amount of

expansion is usually less than the original contraction. The variables associated with the ex- pansion and the residual contraction of concretes have not been well established. Because

of this lack of knowledge studies were also

made of the expansion and the residual contraction of the concretes as well as various

shrinkage-expansion ratios using the same

specimens, employing the statistical procedures

which have been used throughout this series of

articles.

Because of the limited quantities of the different cements, it was not possible to study all of the known variables. The investigation was

limited to the determination of the effects on

shrinkage and expansion of the physical and

chemical properties of the cements and the air

contents of two series of concretes, one made

with a constant water/cement ratio and the

other with a, 5 ± 1-in slump.

2. Materials

2.1. Cements

The cements used in this investigation have

previously been described. The frequency distributions of the results of chemical analyses

as well as spectrochemical analyses were re- ported in section 1, part 1 of this series of

articles [3]. Other tests with these cements

have been reported in parts 2 and 3 of this

series of articles [4] [5] , and the variables associated with the shrinkage characteristics of

the neat portland cement pastes were presented

in the previous section (see page 1). Most of

the 199 commercial portland cement were obtained from different areas of the United

States, but a few were from other countries.

The cements were classified as to type, principally on the basis of chemical and physical

properties ^.

3. Methods of Test

3.1. Preparation of Concretes

The details of the proportioning and mixing

of the concretes were described in part 1, sec- tion 1 of this series of articles [3].

Two series of concretes were made with

these cements. One series, (Series 0), was made with a constant water/cement ratio

(w/c) of 0.635. A second series, (Series A), was made in which the water was varied, if necessary, to obtain a concrete with a 5 ± 1-in

slump. In both series, the cement-to-aggregate

weight ratio was constant. The quantities of

cement and aggregate per unit volume of concrete varied to some extent from the nominal

51/2 bags of cement per cubic yard as designed,

primarily because of variations of the en- trained and entrapped air. The variations of

the cement content will be reported in a later

subsection. The mixing and placing of the concretes were performed at 73 °F.

3.2. Test Specimens

The 6 X 8 X 16-in concrete blocks used for

the shrinkage and expansion measurements are shown in figure 10-1. They were cast in plasticlined, paraffined-hardwood molds. The sides

and bottoms of the molds were bolted together

using heavy graphite grease in all joints to prevent leakage or loss of water. No oil or

grease was used on the plastic liner. Metal

frames fastened to the molds were used to hold

the gage points (5/16 X lV2-in phosphor-bronze

bolts) in position, 10 in, center to center, in

2 On the basis of this classification there were 82 Type I, 8 Type

lA, 68 Type 11, 3 Type IIA, 20 Type III, 3 Type IIIA, 3 Type IV, and 12 Type V cements.

38
25.4

NOTE - ALL DIMENSIONS IN CENTIMETERS

Figure 10-1. Design and dimensions of specimen used for determining shrinkage and

expansion values of concretes made from different cements.

(The purpose of the depression in the one side was to retain water and ice when specimens were placed with this side up in later outdoor exposure tests).

the top and bottom of the concrete block as

i cast until the molds could be stripped. (The

i concrete blocks were made for outdoor exli posure tests after completion of the laboratorymeasurements, and the purpose of the 2-in depression in the one side was to hold rain,

I melted snow, and ice in the weathering test).

I Two specimens were made from each of the

cements, one of each of the two series of concrete, the one with a water/cement ratio of

1 0.635 and the other with a 5 ± 1-in slump. Each

specimen was cast with a 6 X 16-in side as a

base. The 8-in depth of concrete was placed in

three layers, and each layer was tamped 25

times with a %-in diameter bullet-nosed tamping rod. The sides of the mold were spaded

after each layer, and the mold was tapped vig-

*] orously to remove entrapped air.

3.3. Storage of Specimens

The concrete specimens remained in the

molds covered with wet burlap for the first 24

hr. After stripping the molds, drilling the gage

holes, and making length and weight measurements, the specimens were placed in a fog room

at 100 percent relative humidity for 13 days.

The concrete specimens were then placed on

end with five sides exposed to laboratory air at

73 °F and 50 ± 5-percent relative humidity for

8 weeks. They were then immersed in water at

73 °F for 4 weeks.

3.4. Shrinkage and Expansion Measurements

The gage holes were drilled in the phosphorbronze bolts after the molds were stripped at about 24 hr. A 10-in gage-length Whittemoretype strain gage together with an invar-steel

reference bar was used to measure changes in

the distances between the gage holes in both

the tops of the specimens as cast as well as the

gage holes in the bottoms of specimens as cast. The first measurements were made as soon as

possible after removal from the molds. Measurements were also made after the concrete

specimens had been stored as indicated in par.

3.3. The length changes as determined by means

of the Whittemore gage were multiplied by 10

to arrive at values for percentage length

change.

The percentage shrinkage was calculated

from the diiference between the measurements

made after storage in the fog room and those

made after the additional 8 weeks in laboratory

air. The calculated values for percentage

shrinkage will generally be referred to simply

as shrinkage or shrinkage values. The percent39
age expansion was calculated from the differ- ences between the measurements made after

the 8 weeks in laboratory air and those made

after the subsequent 4 weeks in water. The

calculated values for percentage expansion will

generally be referred to simply as expansion or expansion values.

The averages of the top and bottom measure- ments were used in calculating the shrinkage

and expansion value unless otherwise stated.

The values reported were for a single specimen

except for those cements where the use of a

v//c of 0.635 resulted in a slump of 5 ± 1 in, in

which case the average of the two specimens was used.

3.5. Weight Loss and Gain

At the times that length measurements were

made, the specimens were also weighed. The

percentage weight loss was calculated from the

weight after the moist-air storage and the

weight after the 8-week drying in laboratory

air. The percentage weight-gain was calculated from the weight of the specimen after

drying in laboratory air for 8 weeks and the

weight after the subsequent 4 weeks in water.

It was noted that there was generally a

slight weight gain (and also expansion) of the

specimens in the 13 days of moist-air storage.

This gain may have occurred because of inadequate moist curing during the first 24 hr, or because of loss of weight during the period

after the molds were stripped and the gage

holes drilled and initial measurements made

and before the specimens were placed in the

fog room.

4. Abbreviations

The abbreviations, notations, etc. used in this

section for chemical and physical properties are the same as those used in previous sections

of this series of articles ^. In this section, the prefix "0" of the fourletter titles for the various dependent variables

refers to the concretes of Series 0 in which a water/cement ratio of 0.635 was used. The prefix "A" refers to the concretes of Series A

which had a 5 ± 1-in slump. A summary of the

abbreviations for the dependent variables used

in this section are as follows

For Series 0 concretes made with a water/

cement ratio of 0.635:

OSHR = percentage shrinkage after 56 days

drying in laboratory air following

14 days curing in a fog room.

OEXP = percentage expansion after 28 days

water storage following the 14 days

moist-air curing and 56 days drying in laboratory air. ODSX = OSHR minus OEXP = residual

shrinkage.

OREX =: OEXP/OSHR.

OEXR= (OSHR minus OEXP) /OSHR) =

ODSX/OSHR.

ODSH = percentage shrinkage of the top of

the specimen as cast minus the percentage shrinkage of the bottom as

cast. For Series A concretes having a 5 ± 1-in

slump the letter "A" is used instead of "0" as ASHR, AEXP, ADSX, AREX, AEXR, and

ADSH for the dependent variables.

5. Statistical Analyses

The statistical techniques used to find and

evaluate the independent variables associated

with the shrinkage, expansion, the differences,

and the ratios, have been described in a previ- ous section of this series on "Materials and

Techniques" [3]. The statistical treatment was

the same as that used in all previous sections

of this series of articles. Multiple regression

equations were calculated by a least-squares

method using various independent variables to determine which showed an association with

each of the dependent variables. As in previous

sections equations were calculated for both the

AE + NAE cements and the NAE cements.

Calculations were made using only commonly

determined variables and also using these to3 These abbreviations include the use of C3A, C3S, C2S, and C4AF for the calculated potential compounds, tricalcium aluminate,

tricalcium silicate, dicalcium silicate, and tetracalcium aluminoferrite, respectively. Also used are Insol for insoluble residue. Loss

for loss on ignition, APF for air permeability fineness, Wagn for Wagner Turbidimeter fineness. AE -|- NAE refers to air-entraining

plus non-air-entraining cements, and NAE to the non-air-entraining cements.

gether with minor and trace elements.

Ratios of reduction in variance to original

variance ("F" ratios) obtained by fi.tting equations were calculated for two kinds of cases:

(1) for equations including a few main independent variables as compared to the original

data on the dependent variables, or (2) for

equations in which additional independent variables were included as compared to a previous

equation with fewer variables The calculated

"F" ratios and critical "F" values which must

be equalled or exceeded for significance at the

* statistical terms and notations employed in this section are the same as those used in previous sections of this series of articles. For example, S.D. refers to the estimated standard deviation cal- culated from the residuals of a fitted equation, or the estimated standard deviation about the average. Also, as in previous sec- tions, s.d. refers to the estimated standard deviation of a coefficient of an independent variable used in a fitted equation. The

term coef./s.d. is the ratio of the estimated coeflBcient (of an inde- pendent variable used in an equation) to its estimated standard

deviation. "F" designates Fisher's ratio of variances and D.F. is used to designate the number of degrees of freedom. As indicated in previous sections, a coef./s.d. ratio greater than one was considered

to be of sufficient significance to vv'arrant further investigation. /

40
I a = 0.05 and a = 0.01 probability levels are summarized in a table (table 10-44).

After equations had been developed in which

independent variables were significantly asso-

! ciated with the dependent variables, the residuals of these equations were fitted by a least- squares method to other single independent

variables and the reduction in variance calculated. If any of the additional independent variI ables indicated a significant reduction in varij ance, they were tried in the equation and

retained if the coef./s.d. ratio was greater

than 1. Equations were also computed for the "odds"

and "evens" in the array of cements. Comparisons were made of the coefficients of the variables in the two groups of data, and these were

compared to the coefficients and coef./s.d. ratios

computed for all the cements.

Although shrinkage and expansion measure- ments were made on all 199 cements, the cal- culations of the equations presented in this

section were limited to those for which trace- element determinations had been made. The

calculated relationships of the shrinkage and

expansion of the concretes to the dynamic modulus of 3 X 4 X 16-in concrete specimens, or to the shrinkage and cracking characteristics of

neat cement pastes, included all the cements for

which values were available except the three

white cements and the cement having a high

autoclave expansion. A few other cements that

had large deviations from the calculated relationships, for no apparent reason, were also

excluded.

Equations presented in this article were se- lected from a large number of trial equations

indicating the calculated relationship of various

independent variables to the shrinkage and ex- pansion values, their differences, and their

ratios ^ A summary of the relationships indicated by the equations for both series of concretes will be given in the discussion in subsection 7. Some of the limitations on interpretations of

multivariable regression equations as well as other statistical techniques used in this series

of articles have been discussed in section 1,

subsections 4.2., 4.3., and 5 [3]. Other limitations and problems of interpretation have also

been discussed in other subsections of this

series of articles.

6. Results of Tests

6.1. Cement Content of Concretes

The frequency distribution of the cements

with respect to the cement content of the Series

0 concretes made with a water/cement ratio of

0.635 is presented in table 10-1. In table 10-2

is presented similar information with respect

to the Series A concretes made with a slump of

5 it 1 in. It is apparent, from these tables, that

concretes made with the air-entraining cements

had cement contents considerably lower than

the originally designed mix. The cement contents were also, in most instances, lower than

those of the concretes made with the non-airentraining cements. The possible effects of differences of cement content on shrinkage and

expansion will be discussed in a later subsection. The subject is introduced at this time in

view of the fact that cement content may be a

variable which must be considered in the

analyses of the results of shrinkage and expansion measurements made on these concrete

specimens. With a fixed cement to aggregate

weight ratio, the entrained and entrapped air

affected the weight per cubic foot of the freshly

mixed concrete. The air content also affected

the calculated cement factor. Of the two related

variables (air content and cement factor), the

air content was used as one of the independent

variables in equations relating various independent variables to each of the dependent variables.

^ These equations were selected primarily to indicate the associa- tion with commonly determined independent variables having coef./

s.d. ratios greater than one when used in multivariable equations, and also to indicate which of minor and trace elements may have an effect. Table 10-1. Frequency distribution of cements with respect to cement content, in bags per cubic yard, of concretes made with a water- cement ratio of 0.636

Cement content, bags per cubic yard of concrete

4.90 4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 Type cement to to to to to to to to to to to to to Total

4.95 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55

Number of cements

I 2 20 38 21 1 82

868

320

3

15

IA 1 1 4 2

11 1 4 5 18 39 1 IIA 1 1 1 m 1 2 10 7 niA 2 i IV, V 2 8 5

Total 1 0 2 4 5 0 2 1 7 29 74 72 2 199

41
Table 10-2. Frequency distribution of cements with respect to cement content in bags per cubic yard of concretes with a5 ± 1 in. slump

Type cement

Cement content, bags per cubic yard

Total

4.90

to 4.95

4.95 to

5.00

5.00

to 5.05

5.05

to 5.10

5.10

to

5.15

5.15

to 5.20

5.20

to 5.25

5.25

to 5.30

5.30

to 5.35

5.35

to 5.40

5.40

to 5.45

5.45

to 5.50

5.50

to 5.55

Number of cements

5 27 31 16 79

8

66

320

3

15

T A 1 1 3 3

1 1 6 24 31 3

11A 1 1 1 2 3 13 2

1 2

1 5 9

Total 1 1 1 0 3 5 1 3 8 37 73 58 3 194

6.2. Drying Shrinkage of Concretes

a. Drying Shrinkage of Series O Concretes having a water/cement ratio of 0.635 (OSHR)

The frequency distributions of the cements

of the different types with respect to shrinkage

of the Series 0 concretes are presented in table

10-3. The concretes were all made with a water/cement ratio of 0.635, moist cured for

14 days, and then placed in laboratory air for

56 days. The concretes made of the air-entraining cements generally had greater shrinkage

values than the overall average of 0.030. There was a fairly broad distribution of values and

an overlapping of the values for concretes made

of the different types of NAE cements. The

values for the AE cements also overlapped the

values for the NAE cements.

Equations relating the shrinkage of the Series 0 concrete specimens made of AE + NAE

cements to various independent variables are presented in table 10-4. Equation 1 indicates

that there was a significant relationship between the shrinkage and the percentage weight

loss after 56 days exposure to laboratory air. (See also table 10-44)6.

' Eq 0 as used in table 10—44 refers to the S.D. value of the corresponding dependent variable as indicated in footnotes in the

tables of equations.

A number of commonly determined variables were found to have coef./s.d. ratios greater

than 1 when used in a multivariable equation.

These are presented in eq 2, and, by reference

to table 10-44, it may be noted that a highly

significant reduction in variance was attained.

With the additional use of the trace elements

SrO, Zn, and Zr in eq 3 there was a further

significant reduction in the S.D. value. The

equations calculated for the "odds" and "evens"

in the array of cements (eqs 3A and 3B) indicated that C.sS, Na20, and Zn had coef./s.d.

ratios less than 1 in one or the other of the

smaller groups and that Zr had a reversal of

the sign of the coefficient

With the use of AI0O3 and Fe203 in eq 4 instead of the potential compounds as in eqs 2

and 3, a highly significant reduction in the

S.D. value was also attained (see also table

' If a number of cements having higher than normal values for an independent variable are included in one of the two groups (the "odds" or "evens") by the arbitrary division of the cements, this distribution may result spurious coefficients for the variable. If the

coefficients of both "odds" and "evens" of an independent variable are significant, a greater confidence can be placed in the equation, and in the association of that independent variable with the de- pendent variable. If the coefficient for a variable in either the "odds" or "evens" is not greater than its s.d., some consideration may still be given to the larger groups of cements as indicating a possible relationship.

Table 10-3. Frequency distribution of the cements with respect to shrinkage of concretes made with a water-cement ratio of 0.635

moist-cured for 14 days, then dried in laboratory air for 66 days (OSHR)

Type cement

Percentage shrinkage

Total

0.014

to 0.017

0.017

to 0.020

0.020

to 0.023

0.023

to 0.026

0.026

to 0.029

0.029

to 0.032

0.032

to 0.035

0.035

to 0.038

0.038

to 0.041

0.041

to 0.044

Number of cements

r.... 2 2 2 5 11 23

1 11

18 144

4

2

5

11

5

14

828

68

220

3

15

lA 2

II 2 IIA

1 1 4 9 19 13

III 2 2 4 1

11

5 1 IIIA 1 IV, V 1 2 4 3 1 2

Total 3 4 10 20 37 38 37 31 11 7 198

42
I 10-44). With the additional use of the trace

I elements SrO, Zr, and Zn in eq 5 there was a

reduction in variance, significant at the 5-percent probability level. The coef./s.d. ratio for

Zn was less than 1 in eq 5A for the "odds" in

the array of cements and the coef. for Zr had a

reversal of sign. The coefficients of neither were

highly significant in eq 5 where all cements were included in the calculations.

Table 10-5 presents a corresponding series

of equations for the shrinkage of Series O concretes made of the NAE cements. The air content did not have a coef./s.d. ratio greater than

1 in the equations calculated for these cements,

but this variable was highly significant in the

previous table where the AE cements were inI volved. The shrinkage was probably significantly related to the percentage weight loss of

the concretes made of the different cements as

j indicated in eq 1 of table 10-5. The use of com-

|i monly determined independent variables in eqs

: 2 and 4 resulted in highly significant reductions

! in the S.D. values. The additional use of the

1 trace elements SrO, Zr, and Zn in eqs 3 and 5

' resulted in a possibly further reduction in the

i S.D. values (see also table 10-44) significant at

1 the 5-percent probability level. It may be noted

that in equations for the "odds" and "evens"

I (eqs 3A, 3B, 5A, and 5B) that C3S, FeaOs, SrO,

I Zr, and Zn each had coef./s.d. ratios less than 1 in one or the other of the equations for the

j smaller groups of cements. The coefficients of

,j these independent variables were generally not

highly significant when the larger groups of

I cements were used in the calculations in eqs

j 3 and 5.

j Coefficients of the independent variables in

1 eq 3 of table 10-5 and the approximate ranges

of these variables were used to determine their

calculated contributions to the shrinkage of the

constant w/c concretes, as well as the ranges

of such contributions. These are presented in

i table 10-6 ^. These calculated values are esti-

} mates based on a single equation, and somewhat

: different values would be obtained by use of

other equations.

\ It may be noted in tables 10-4, 10-5 and

10-6 that increases in C3A, C4AF, and fineness

of the cements were associated with increases

in shrinkage values. Increases in NaaO, SO3,

and loss on ignition were associated with deI creases in the shrinkage values. It is indicated

I in table 10-6 that differences in C3A, fineness,

^ and SO3 show the greatest calculated effect on

I the shrinkage of the concretes. As previously

I indicated, the coefficient for the air content was

highly significant when air-entraining cements

! « Corresponding tables for equations calculated for NAE cements.

i using the calculated potential compounds, other commonly deter- mined variables, and trace elements having coef./s.d. ratios greater than 1 will be presented for other dependent variables. A summary

table (table 10-45) is also presented for greater ease in comparing

J similar equations for AE + NAE cements.

were included in the calculated equations as in

table 10-4.

b. Drying Shrinkage of Series A Concretes having a

5 ± 1-in. Slump (ASHR)

The frequency distributions of the cements

of the different types with respect to shrinkage

of the Series A concretes (ASHR) are presented in table 10-7. There was a broad distribution of results and an overlapping of the

cements of the different types. It was previously indicated in table 2-12 of section 2 of

this series of articles [3] , that the air-entraining cements. Types lA, IIA, and IIIA, had

slump values greater than 5 ±: 1 in when made

with a constant water/cement ratio. Although

the water/cement ratio for these cements was

reduced for the Series A concretes, most of

these concretes were, as shown in table 10-3,

in the upper half of the frequency distribution.

The frequency distribution of the water/

cement ratios required for the Series A concretes was previously presented in table 2-17

in section 2 of this series of articles [3]. The

w/c ranged from about 0.55 to 0.70. Equations are presented in table 10-8 for

AE + NAE cements indicating the relationships between the shrinkage of the Series A

concretes and the various independent variables. Equation 1 gives no significant indication

of a relationship between the water/cement

ratio required for the concretes with a 5±: 1- in slump and the shrinkage. There was a relationship, significant at the 5-percent probability

level, between the shrinkage and the percentage

weight-loss of the specimens of the different concretes. Using commonly determined independent variables in eqs 3 and 5 resulted in

highly significant reductions in the S.D. values

(see also table 10-44). The additional use of

the trace elements SrO, Zr, and Zn in eq 4 or

Co, SrO and Zn in eq 6 resulted in reductions

of the S.D. values, each significant at the 5-percent probability level. All of these trace ele- ments had coef./s.d. ratios less than 1 in one

or the other of the equations for the "odds" or

"evens", eqs 4A, 4B, 6A, and 6B. The coef./s.d.

for C3S was also less than 1 in eq 4B,

Corresponding equations for the NAE ce- ments are presented in table 10-9. The coef,/

s.d. ratio for "air content" was less than 1 in

equations for the NAE cements. The use of

w/c as an independent variable in eq 1 did not

result in a significant reduction of variance.

The use of commonly determined variables in

eqs 3 and 5 resulted in highly significant reductions in the S.D. value. The additional use of

trace elements SrO, Zr, and Zn in eq 4 or Co,

Zr and Sn in eq 6 resulted in a reduction of the

S.D. value at the 5-percent probability level (see table 10-44). In equations for the "odds"

and "evens" there were instances where each

43
Table 10-4. Coefficients for equations for AE+NAE cements relating OSHR, the percent nominal 5Yz bags of cement per cubic yard and a water

Equation Note Const. CaA C4AF AI2O3

(•)

(')

(>)

(.')

(.')

()

(')

{')

(')

OSHR =+0.0208

s.d. = (0.0028) OSHR =+0.0130

s.d. = (0.0040) OSHR =+0.01.'?9

s.d. = (0.0039) OSHR (odd) =+0.0178

s.d. = (0.0056) OSHR (even) =+0.0076

s.d. = (0.0058) OSHR =+0.0098

s.d. = (0.0033) OSHR =+0.0104

s.d. = (0.0033) OSHR (odd) =+0.0114

s.d. = (0.0048) OSHR (even) =+0.0100

s.d. = (0.0050)

+0.00136

(0.00013) + 0.00123

(0.00014) +0.00126

(0.00020) +0.00111

(0.00022)

-0.0000765

(0.0000529) -0.0000835

(0.0000517) -0.0001413

(0.0000684) *+ 0.0000746

(0.0000890)

+0.000926

(0.000174) +0.000898

(0.000171) +0.000847

(0.000241) +0.000998

(0.000260) +0.00358

(0.00035) +0.00323

(0.00038) +0.00345

(0.00055) +0.00307

(0.00055)

' 177 cements; Avg = 0.03028; S.D. = 0.005832. 2 89 cements. « 88 cements. * Coef./s.d. ratio less than 1.

Table 10-5. Coefficients for equations for NAE cements relating OSHR, the percentage

6}/2 bags of cement per cubic yard and a water-cem

Equation Note Const. CaA CaS C4AF

1..

2..

3..

3A.

3B.

4..

5..

5A

5B

(•)

(')

(')

{') m

(•)

(')

{')

(«)

OSHR

s.d. = +0

= (0 0214

0028) OSHR

s.d. = +0

= (0 0157

0040) OSHR

s.d. = +0

= (0 0164

0040) OSHR (odd)

s.d. = +0

= (0 0159

0055) OSHR (even)

s.d. = +0

= (0 0143

0058) OSHR

s.d. = +0

= (0 0123

0034) OSHR

s.d. = +0

= (0 0127

0033) OSHR (odd)

s.d. = +0

= (0 0076

0049) OSHR (even)

s.d. = +0

= (0 0170

0049)

+0.001.35 -0.0000775 +0.000866

(0.00013) (0.0000534) (0.000172) +0.00123 -0.0000860 +0.000846

(0.00014) (0.0000522) (0.000170) +0.00124 -0.0001790 +0.001023

(0.00020) (0.0000638) (0.000253) +0.00105 *+ 0.00008 14 + 0.000687

(0.00021) (0.0000918) (0.000233)

> 165 cements, Avg = 0.0297P percent; S.D. = 0.005636. = 83 cements. ^ 82 cements. * Coef./s.d. ratio less than 1.

44
age shrinkage after 66 days drying following 14 days moist curing of concretes having a

-cement ratio of 0.635, to various independent variables

i>J ii,2\J IjOSS APF Air content Zr orw Zn 1 Percent

j wt loss S D

+0.00355

(0.00106) 0.005668

-0.00683

(0.00192) -0.00822

(0.00198) -0.01027

(0.00246) *- 0.00275

(0.00361 -0.00648

(0.00191) -0.00783

(0.00197) -0.01008

(0.00251) -0.00.363

(0.00345)

-0.00853

(0.00115) -0.00894

(0.00114) -0.00961

(0.00172) -0.00863

(0.00164) -0.00836

(0.00114) -0.00876

(0.00114) -0.00908

(0.00174) -0.00864

(0.00164)

-0.00369

(0.00065) -0.00363

(0.00065) -0.00.502

(0.00121) -0.00317

(0.00085) -0.00372

(0.00065) -0.00365

(0.00065) -0.00537

(0.00122) -0.00317

(0.00085)

+0.00000589

(0.00000080) +0.00000613

(0.00000078) +0.00000708

(0.00000125) +0.00000510

(0.00000107) +0.00000549

(0.00000075) +0.00000568

(0.00000074) +0.000006.32

(0.0000012.3) +0.00000550

(0.00000096)

+0.00105

(0.00018) +0.00100

(0.00018) + 0.00101

(0.00024) +0.00108

(0.00027) +0.00106

(0.00018) +0.00102

(0.00018) +0.00101

(0.00024) +0.00104

(0.00027)

0.004108 +0.0126

(0.0081) -0.0679

+0.0093

(0.0090)

+0.008.54 (0.00407) +0.00772

\yj . UUO lUJ +0.00860

(0.00604)

-0.0198

(0.0098) *-0.0145

(0.0199) -0.0222

(0.0119)

0.004005

0.003942

0.004106

+0.000702

(0.000436) +0.000848

(0.000429) +0.000813

(0.000816) +0.000988

(0.000645)

0.004121

+0.0119

(0.0081) -0.0847

(0.0490) +0.0103

(0.0089)

+0.008.57

(0.00409) +0.00671

(0.00627) +0.00793

(0.00600)

-0.0190

(0.0099) *-0.0112

(0.0202) -0.0221

(0.0119)

0.004025

0.004022

0.004100

shrinkage after 56 days drying following H days moist curing of concretes having a nominal

ent ratio of 0.635, to various independent variables

NaaO SO 3 Loss APF Zr SrO Zn Percent wt. loss S.D.

+0.00283

(0.00106) 0.005502

-0.00665

(0.00190) -0.00795

(0.00196) -0.00906

(0.00235) -0.00393

(0.00357) -0.00627

(0.00189) -0.00749

(0.00195) -0.00821

(0.00243) -0.00453

(0.00350)

-0.00874

(0.00114) -0.00917

(0.00113) -0.00923

(0.00164) -0.00895

(0.00167) -0.00856

(0.00113) -0.00896

(0.00113) -0.00875

(0.00171) -0.00905

(0.00166)

-0.00376

(0.0006.5) -0.00367

(0.00066) -0.00484

(0.00103) -0.00344

(0.00089) -0.00380

(0.00065) -0.00371

(0.00066) -0.00475

(0.00108) -0.00334

(0.00088)

+ 0.00000593

(0.00000080) +0.00000619

(0.00000078) + 0.00000778

(0.00000128) +0.00000610

(0.00000105) +0.00000554

(0.00000076) +0.00000575

(0.00000074) + 0.00000683

(0.00000129) +0.00000502

(0.00000094)

0.004022

+0.0118

(0.0080) +0.0441

(0.0204)

* +0.0017

(0.0093)

+0.00784

(0.00414) *+0. 00312

(0.00605) +0.01.367 (0.00619)

-0.0209

(0.0096) -0.0.309

(0.0116) *-0.0129

(0.0174)

0.003920

0.003732

0.004013

+0.000558

(0.000429) +0.000710

(0.000422) +0.001365

(0.000659) *+0. 000120

(0.000569)

0.004034

+0.0111

(0.0080) +0.0425

(0.0214) *+ 0.0028

(0.0092)

+0.00-,oj (0.00417) *+0. 00171

(0.00631) +0.01266

(O.00B09)

-0.0202

(0.0097) -0.0285

(0.0121) *-0.0140

(0.017.5)

0.003941

0.003905

0.004007

45
Table 10-6. Calculated contributions of independent variables

to the percentage shrinkage after 66 days drying following H

days moist curing of concretes having a nominal 5 ' ^ hags of cement per cubic yard and a water-cement ratio of 0.636, and

the calcidated ranges of such contributions (OSHR)

Indepenfient

variables

xtange 01 varifibles (percent)

v^oelticients from ec[ (3)

T-HOlc i-U O

Calcul&tefi con.tri~ hntmnH to O.SH'R

Calculat- ed ranges

of contribii tions to OSHR

Cf\rtRi —-1-0 0164

0 to 15 0 to +0.0184 0 0184 CsS** 20 to 65 -0.000086 -0.0017 to -o!o060 0]0043 C4AF ... 4 to 17 -f 0.000846 +0.0034 to +0.0144 0.0110 NaaO 0 to 0.75 -0.00795 0 to -0.0060 0.0050 SO3 1.2 to 3.0 -0.00917 -0.0110 to -0.0275 0.0165 Loss 0.3 to 3.3 -0.00367 -0.0011 to -0.0121 0.0110 APF *2500 to 5500 +0.00000619 +0.0155 to +0.0340 0.0185

Zr** 0 to 0.5 -1-0.0118 0 to +0.0059 0.0059 SrO** 0 to 0.4 4-0.00784 0 to +0.0031 0.0031 Zn 0 to 0.2 -0.0209 0 to -0.0042 0.0042

*cra2/g. Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

of these trace elements as well as C3S had coef./

s.d. ratios less than 1 in one or the other of

the smaller groups of cements.

Calculated contributions and ranges of con- tribution to the shrinkage of the variables in

eq 4 table 10-9, together with the ranges of the

variables, are presented in table 10-10, In- creases in C3A, C4AF, and fineness were asso- ciated with increased shrinkage. Increases in

NaoO, SO3, Loss, and possibly Zn were associated with decreases in the shrinkage values.

Of these, differences in fineness, C3A and SO3

had the greatest calculated effect on shrinkage.

Table 10-7. Frequency distribution of the cements with respect to shrinkage of concrete having a nominal 6Y2 ^0.9^ of cement per cubic yard and a 6 dz 1 in. slump, moist-cured for I4 days, then dried in laboratory air for 66 days (ASHR)

Percentage shrinkage

Type cement

0.014

to 0.017

0.017

to 0.020

0.020

to 0.023

0.023

to 0.026

0.026

to 0.029

0.029

to 0.032

0.032

to 0.035

0.035

to 0.038

0.038

to 0.041

0.041

to 0.044

0.044

to 0.047 Total

Number of cements

I 1 3 2 3 13 20 18 13 4 1 78 lA 3 3 2 8 n 3 4 14 16 9 9 5 4 2 66 IIA 1 1 2

III 1 1 3 1 3 4 5 2 20

IIIA 1 1 1 3

TV. V _ _ _ 1 6 4 1 1 1 1 15

Total 1 7 8 26 35 34 34 27 14 5 1 192

Table 10-8. Coefficients for equations for AE-\-NAE cements relating ASHR, the percent nominal 6}/^ bags of cement per cubic yard and a

1...

2...

3...

4...

4A.

4B.

5..

6..

6A.

6B.

Equation Note

(')

(')

(')

(')

(»)

(')

(')

(')

(')

Const

ASHR

s.d. ASHR

B.d. ASHR

s.d. ASHR

s.d. ASHR (odd) -- s.d. ASHR (even) = s.d. ASHR

s.d. ASHR

s.d. ASHR (odd) = s.d. ASHR (even) = s.d.

^+0.0363

= (0.0113)

= +0.0218

= (0.0029)

= +0.0118

= (0.0040)

= +0.0129

= (0.0040)

= +0.0192

= (0.0060)

= +0.0046

= (0.0058)

= +0.0083

= (0.0034)

= +0.0099

= (0.0033)

= +0.0113

= (0.0052)

= +0.0075

= (0.0048)

CaA

+0.001358

(0.000135) + 0.001221

(0.000146) +0.001162

(0.000206) +0.001159

(0.000228)

CaS

-0.0000835

(0.0000535) -0.0000903

(0.0000524) -0.0001644

(0.0000711) *+ 0.0000590

(0.0000902)

C4AF

+0.000942

(0.000176) + 0.000918

(0.000174) +0.000861

(0.000264) +0.000997

(0.000243)

AhOz

+0.00357

(0.00036) +0.00315

(0.00038) +0.00318

(0.00056) +0.00310

(0.00056)

» 171 cements; Avg = 0.03000 percent; S.D. = 0.005648. 2 86 cements. a 85 cements. Coef./s.d. ratio less than 1.

46
6.3. Expansion of Concretes as a Result of

Rewetting

a. Expansion of Series O Concretes made with a water/

cement ratio of 0.635. Air-dried and then Rewetted

(OEXP)

After 14 days moist-air curing, then drying

in laboratory air for 8 weeks, the concrete

specimens were placed in water for 28 days.

The frequency distribution of the expansion

values of the Series 0 concretes made of the

different cements is presented in table 10-11.

A comparison of table 10-11 for expansion and

table 10-3 for shrinkage of the Series 0 concretes shows that the range of values for the

expansion was not so great as the range of

values for the shrinkage. The expansion values

of the air-entraining cements, were generally

above the average for all cements in table

10-11 and the shrinkage values appeared to be still further above the average shrinkage for

all cements in table 10-3. There was an over- lapping of the expansion values of the cements

of the different types in table 10-11.

Equations for AE + NAE cements are presented in table 10-12 indicating the relationship of the expansion values of Series 0

concretes (OEXP) to various independent

variables. Equation 1 indicates at the 5-percent

significance level that there is a probable relationship between the expansion and the percentage weight-gain of the rewetted concrete

specimens made of the different cements. The

use of commonly determined independent variables in eqs 2 and 4 resulted in highly significant reduction in th 3.D. values, (see also

table 10-44). By the additional use of the trace

elements, P, Pb, Kb, SrO and Zn in eqs 3 and 5, a further significant reduction in the S.D. value was achieved. It may be noted that in equations

for the "odds" and "evens", all of these trace elements except Kb, had coef./s.d. ratios of less than 1 in one or the other of the equations for

the smaller groups of cements, see eqs 3A, 3B,

5A and 5B.

A corresponding series of equations for the

NAE cements is presented in table 10-13. The

relationship of the expansion values to the percentage weight-gain resulting from soaking 28

days in water is presented in eq 1. By reference

to table 10-44 it may be noted that the indication of relationship is not significant at the

5-percent probability level. The coef./s.d. ratio

for the air content was less than 1 for the NAE

cements, and this variable was not included in

the equations. The use of commonly determined

variables in eqs 2 and 4 resulted in highly significant reductions in the S.D. values, (see

table 10-44). The use of trace elements P, Pb,

Kb, SrO, and Zn in eqs 3 and 5 resulted in further significant reductions in the S.D. values.

In the equations for the "odds" and "evens"

(eqs 3A, 3B, 5A and 5B) Pb, and SrO, as well as CaO, had coef./s.d. ratios less than 1 in one

or the other of the pairs of equations with the

smaller groups of cements.

Calculated contributions of the different variables to the expansion after 28 days rewetting,

as well as the estimated ranges of such contributions are presented in table 10-14. It may be

noted that increases in fineness, C3A, C4AF, Rb,

and possibly P were associated with increases

in the expansion values. Increases in SO3 and

age shrinkage after 56 days drying following I4 days moist curing of concretes having a slump of 6 1 in., to various independent variables

NajO SO3 Loss APF Air

content Zr SrO Zn Co W/C Percent wt loss S.D.

*-0.0099

(0.0177) 0.005659

+0.00305

(0.00105) 0.005530

-0.00595

(0.00194) -0.00714

(0.00199) -0.00578

(0.00311) -0.00858

(0.00276) -0.00556

(0.00193) -0.00640

(0.00197) -0.00415

(0.00314) -0.00756

(0.00267)

-0.00737

(0.00117) -0.00784

(0.00117) -0.00827

(0.00179) -0.00673

(0.00171) -0.00721

(0.00677) -0.00768

(0.00116) -0.00741

(0.00184) -0.00709

(0.00167)

-0.00392

(0.00066) -0.00381

(0.00067) -0.00359

(0.00123) -0.00415

(0.00089) -0.00393

(0.00117) -0.00377

(0.00066) -0.00379

(0.00124) -0.00409

(0.00087)

+0.00000588

(0.00000081) + 0.00000609

(0.00000079) +0.00000594

(0.00000131) +0.00000555

(0.00000107) +0.00000543

(0.00000076) +0.00000544

(0.00000075) +0.00000490

(0.00000133) +0.00000575

(0.00000093)

+0.000658

(0.000156) +0.000620

(0.000153) +0.000487

(0.000209) +0.000848

(0.000242) +0.000680

(0.000156) +0.000646

(0.000153) +0.000474

(0.000216) +0.000826

(0.000231)

0.004099 +0,00927

(0.00817) *-0. 01896

(0.05798) +0.00982

(0.00934)

+ 0.00828

(0.00420)

* + 0.00638

(0.00647) + 0.01218

(0.00652)

-0.0216

(0.0101) -0.0277

(0.0130) *-0.0099

(0.0178)

0.004002

0.004044

0.004055

0.004113 +0.00884

(0.00413) *+ 0.00386

(0.00665) + 0.01190

(0. 00611)

-0.0145

(0.0102) -0.0246

(0.0143) *-0.0015

(0.0163)

-0.3150

(0.2375) *-0.1099

(0.3058) -0.7669

(0.4421)

0.004015

0.004178

0.003988

47
Table 10-9. Coefficients for equations for NAE cements relating ASHR, the percentage 5 J/2 bags of cement per cubic yard and a slump

Equation Note Const. CsA C3S C^AF AI2O3

1..

2..

3..

4..

4A,

4B

5..

6..

6A

6B,

ASHR = -0

s.d. = (0 ASHR = +0

s.d. = (0 « ASHR = +0

s.d. = (0

(•) ASHR = +0

s.d. = (0 w ASHR (odd) = +0

s.d. = (0

(») ASHR (even) = +0

s.d. = (0

(') ASHR = +0

s.d. = (0

{') ASHR = +0

s.d. = (0

(^) ASHR (odd) = +0

s.d. = (0

(') ASHR (even) = +0

s.d. = (0

+0.001319

(0.000134) +0.001205

(0.000145) +0.001212

(0.000222) +0.001074

(0.000202)

-0.0000871

(0.0000540) -0.0000950

(0.0000528) -0.0001852

(0.0000775) *+ 0.0000337

(0.0000816)

+0.000891

(0.000174) +0.000880

(0.000172) +0.000916

(0.000275) +0.000800

(0.000225) +0.00346

(0.00036) +0.00310

(0.00038) +0.00316

(0.00060) +0.00291

(0.00050)

1 159 cements; Avg = 0.02964 percent; S.D. = 0.005558. 80 cements. ' 79 cements. Coef./s.d. ratio less than 1. Table 10-10. Calculated contributions of independent variables

to the percentage shrinkage after 66 days drying following I4 days moist curing of concretes having a nominal 5'^<2 bags of cement per cubic yard and a slump of 5 ± 1 in., and the cal- culated ranges of such contributions (ASHR)

Table 10-11. Frequency distribution of cements with respect to expansion after 28 days moist storage following 66 days drying

of nominal 6^/2 bags of cement per cubic yard concretes made

with a water-cement ratio of 0.635 (OEXP)

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (4) table 10-9 Calculated contri- butions to ASHR

Calculat- ed ranges

of contri- butions

to ASHR

Const. = +0.0152 CjA 0 to 15 +0.001205 0 to +0.0181 0.0181 CS**--. 20 to 65 -0.0000950 -0.0019 to -0.0062 0.0043 C4AF 4 to 17 +0.00088 +0.0035 to +0.0150 0.0115 NajO 0 to 0.75 -0.00687 0 to -0.0051 0.0051 SO3 1.2 to 3.0 -0.00822 -0.0099 to -0.0247 0.0148 Loss 0.3 to 3.3 -0.00389 -0.0012 to -0.0128 0.0116 APF *2500 to 5500 + 0.00000617 + 0.0154 to +0.0339 0.0185

Zr** 0 to 0.5 + 0.00866 0 to +0.0043 0.0043 SrO** 0 to 0.4 +0.00681 0 to +0.0027 0.0027 Zn 0 to 0.2 -0.0237 0 to -0.0047 0.0047

*cmyg.

**Coefiicient of doubtful significance as coef./s.d. ratio was less than 2.

Percentage expansion

0.011 0.014 0.017 0.020 0.023 0.026 0 029 0.032

Tj'pe cement to to to to to to to to Total 0.014 0.017 0.020 0.023 0.026 0.029 0 032 0.035

Number of cements

I .__ 3 6 19 25 22 6 1 82 lA 2 3 3 8

II 1 13 19 20 11 2 1 1 68

IIA 1 1 2

III 3 3 9 3 2 20

IIIA 1 1 1 3 IV. V 1 3 6 2 1 2 15

Total 5 25 48 59 41 16 3 1 198

Table 10-12. Coefficients for equations for AE-\-NAE cements relating OEXP, the ex 5 bags of cement per cubic yard and a water-ce

Equation Note Const. CsA C^AF CaO Ah03

1..

2..

3..

3A.

3B.

4..

6..

5A.

5B

(')

(')

(')

{')

(')

(')

{')

(.')

OEXP

s.d. OEXP

s.d. OEXP

s.d. OEXP (odd)

s.d. OEXP (even)

s.d. OEXP

s.d. OEXP

s.d. OEXP (odd)

s.d. OEXP (even)

s.d.

^+0.0164

= (0.0018)

= +0.0098

= (0.0023)

= +0.0107

= (0.0022)

= +0.0101

= (0.0031)

= +0.0105

= (0.00.35)

= +0.0394

= (0.0123)

= +0.0380

= (0.0121)

= +0.0310

= (0.0164)

= +0.0464

= (0.0191)

+' .000664

(( .000090) +0.000595

(0.000099) +0.000595

(0.000136) +0.000598

(0.000152)

+ 0.000413

(0.000116) + 0.000390

(0.000115) +0.000390

(0.000165) + 0.000427

(0.000175) -0.000453

(0.000191) -0.000415

(0.000188) -0.000316

(0.000255) -0.000544

(0.000295)

+0.00172

(0.00023) +0.00155

(0.00026) +0.00157

(0.00035) +0.00153

(0.00039)

« 176 cements; Avg = 0.02056 percent; S.D. = 0.003593. 1 cements. * Coef./s.d. ratio less than 1.

48
shrinkage after 56 days drying following 14 days moist curing of concretes having a nominal

of 5 1 in., to various independent variables

NaiO SOa Loss APF Zr SrO Zn Co W/C Percent wt loss S.D.

+0.0489

(0.0232) 0.005499

+0.00.384

(0.00106) 0.005355

-0.00588

(0.00194) -0.00687

(0.00198) -0.00608

(0.00335) -0.00639

(0.00251) -0.00543

(0.00192) -0.00601

(0.00195) -0.00483

(0.00345) -0.00641

(0.00238)

-0.00776

(0.00117) -0.00822

(0.00117) -0.00876

(0.00209) -0.00812

(0.00152) -0.00755

(0.00117) -0.00799

(0.00116) -0.00775

(0.00208) -0.00819

(0.00150)

-0.00403

(0.00067) -0.00389

(0.00068) -0.00431

(0.00125) -0.00381

(0.00081) -0.00406

(0.00067) -0.00.388

(0.00066) -0.00427

(0.00127) -0.00376

(0.00078)

+0.00000594

(0.00000081) +0.00000617

(0.00000080) +0.00000765

(0.00000150) +0.00000492

(0.00000095) +0.00000550

(0.00000077) +0.00000550

(0.00000075) +0.00000610

(0.00000149) +0.00000506

(0.00000085)

0.004024 + 0.00866

(0.00811) +0.02849

(0.0-478) *+0 00301

(0.00822)

+0.00681

(0.00432) +0.00263

(0.00750) +0.01160

(0.00570)

-0.0237

(0.0100) -0.0420

(0.0217) -0.0180

(0.0110)

0.003931

0.004328

0.003603

+0.000710

(0.000436) +0.000926

(0.000430) +0.001129

(0.000709) +0.000590

(0.000559)

0.004040 +0.00697

(0 . 00424) *+0. 00243

(0.00727) +0.01130

(0.00547)

-0.0164

(0.0100) -0.0232

(0.0217) -0.0141

(0.0114)

-0.3628

(0.2426) -0.4419

(0.3592) *-0.2183

(0.3624)

0.003938

0.004459

0.003573

Pansion after 28 days moist curing following 56 days drying of concretes having a nominal

]'i ment ratio of 0.636, to various independent variables

S03 Loss APF Air

content Zn Rb P SiO Pb Percent wt gain S.D.

+0.00163

(0.00070) 0.003549

-0.00394

(0.00078) -0.00411

(0.00076) -0.00380

(0.00103) -0.00415

(0.00131) -0.00435

(0.00079) -0.00444

(0.00077) -0.00402

(0.00105) -0.00473

(0.00133)

-0.00233

(0.00045) -0.00220

(0.00044) -0.00178

(0.00054) -0.00271

(0.00080) -0.00256

(0.00045) -0.00243

(0.00044) -0.00196

(0.00056) -0.00298

(0.00078)

+ 0.00000294

(0.00000051) +0.00000300

(0.00000050) + 0.00000290

(0.00000061) +0.00000315

(0.00000091) +0.00000326

(0.00000052) +0.00000327

(0.00000051) +0.00000310

(0.00000063) +0.00000356

(0.00000092)

+0.000608

(0.000122) +0.000646

(0.000118) +0.000784

(0.000170) +0.000540

(0.000174) +0.000571

(0.000118) +0.000606

(0.000116) +0.000748

(0.000168) +0.000492

(0.000169)

0.002802

-0.0102

(0.0065) *-0.0074

(0.0076) -0.0151

(0.0143)

+0.3234

(0.1150) +0.2485

(0.1807) +0.3601

(0. 1707)

+0.00369

(0.00198) +0.00587

(0.00290)

* +0.00244

(0.00305)

-0.00378

(0.00268) -0.00621

(0.00395) *-0. 00314

(0.00397)

-0.0518

(0.0345) -0.0730

(0.0470) *-0.0248

(0.0537)

0.002711

0.002607

0.002920

0.002779

-0.0099

(0.0064) *-0.0071

(0.00?5) -0.0152

(0.0139)

+0.2853

(0. 1150) +0.2188

(0. 1786) +0.3308

(0.1673)

+0.00406

(0.00196) +0.00593

(0.00283) +0.00326

(0.00303)

-0.00409

(0.00265) -0.00663

(0.00393) *- 0.00329

(0.00:!89)

-0.0499

(0.0341) -0.0677

(0 . 0486) *- 0.0307

(0.0528)

0.002677

0.002588

0.002868

49
Table 10-13. Coefficients for equations for NAE cements relating OEXP, the percentage ex 5Yi bags of cement per cubic yard and a water-ce

Equation Note Const. CaA C4AF CaO A iftO-

(')

(')

(')

(')

(')

(')

(')

OEXP =+0.0176

s.d. = (0.0019) OEXP =+0.0106

s.d. = (0.0024) OEXP =+0.0117

s.d. = (0.0023) OEXP (odd) =+0.0127

s.d. = (0.00.30) OEXP (even) = +0.0108

s.d. = (0.0037) OEXP =+0.0412

s.d. = (0.0126) OEXP =+0.0388

s.d. = (0.0122) OEXP (odd) =+0.0101

s.d. = (0.0159) OEXP (even) = +0.0720

s.d. = (0.0189)

+0.000688

(0.000093) +0.000595

(0.000099) +0.000628

(0.000126) +0.000565

in (1001591

+0.000401

(0.000119) + 0.000368

(0.000115) +0.000251

(0 0001411 +0.000568

fO OOO'QQl

3A - -

3B -

4 -0.000475

(0.000195) -0.000416

(0.000169) *+0.000018

(0.000248) -0.000912

(0.000293)

+0.00179

(0.00024) +0.00157

(0.00026) + .000169

(0.00033) +0.00140

(0.00040)

5 - -

5A -

5B

1 164 cements; Avg = 0.02031 percent; S.D. = 0.003520. 2 32 cements. * Coef./s.d. ratio less than 1.

loss on ignition were associated with decreases

in the expansion values. Of these variables, differences in fineness, C3A, and SO3 had the

greatest calculated effect on differences of ex- pansion of the concretes.

Table 10-14. Calculated contributions to the percentage expansion after 28 days in water following 66 days air-drying of

concretes having a nominal 6Y2 bags of cement per cubic yard

and a water-cement ratio of 0.635, and the calculated ranges of such contributions {OEXP)

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (3) table 10-13

Calculated contri- butions to OEXP

Calculat- ed ranges

of contri- butions.

to OEXP

Const. = +0.0117 C3A 0 to 15 + 0.000595 0 to +0.0089 0.0089 CAF 4 to 17 + 0.000368 + 0.0015 to +0.0063 0.0048 SO3 1.2 to 3.0 -0.00433 -0.0052 to -0.0130 0.0078 Loss 0.3 to 3.3 -0.00214 -0.0006 to -0.0071 0.0065 APF *2500 to 5500 + 0.00000315 +0.0079 to +0.0173 0.0094 Zn** 0 to 0.2 -0.0110 0 to -0.0022 0.0022 Rb 0 to 0.01 + 0.3894 0 to +0.0039 0.0039 P 0 to 0.5 +0.00438 0 to +0.0022 0.0022 SrO** 0 to 0.4 -0.00394 0 to -O.OOlfi 0.0016 Pb**- -- 0 to 0.05 +0.0450 0 to +0.0022 0.0022

*craVg. Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

b. Expansion of Series A Concretes made with a Slump

of 5 ± 1-in., Air-dried and then Rewetted (AEXP)

The frequency distributions of the different

types of cement with respect to the expansion

of Series A concretes (AEXP) are presented

in table 10-15. There was a fairly broad distribution of values and an overlapping of val- ues for cements of the different types.

Equations relating the expansion values of

the concrete specimens made of AE + NAE

cements to various independent variables are presented in table 10-16. Equation 1 indicates

Table 10-15. Frequency distribution of cements with respect to expansion after 28 days moist storage following 56 days of drying of concretes having a nominal 5 '4 bags of cement per cubic yard and a 5 ± 1 in. slump {AEXP)

Percentage expansion

0.011 0.014 0.017 0.020 0.023 0.026 0.029 Type cement to to to to to to to Total 0.014 0.017 0.020 0.023 0.026 0.029 0.032

Number of cements

I 4 4 12 25 24 7 3 79 lA 1 3 4 8

II 1 7 26 16 11 5 66 IIA 1 1 2

III 4 2 5 6 1 2 20

IIIA 1 1 1 3

IV, V 2 6 4 2 1 15

Total 5 17 47 55 47 16 6 193

that there was no apparent relationship between the water/cement ratio required to obtain concretes of 5 ± 1-in slump and the expansion on rewetting the air-dried specimens.

There was an indication, significant at the 5- percent probability level, of a relationship between the expansion and the percentage weightgain of the specimens made of the different

cements as indicated in eq 2 (see also table

10-44). Using only the major potential compounds in eq 3 resulted in a significant reduction in the S.D. value, although the C3S had a

coef./s.d. ratio less than 1 and the coefficient

for C4AF was not highly significant. With the

use of additional commonly determined variables in eq 4, a further significant reduction in

the S.D. value was obtained, (see table 10-44),

and the coefficients for C3S and C4AF were

more highly significant than in eq 3. The additional use of the trace elements Mn, Ni, P, and

50
pansion after 28 days moist curingfollowing 56 days drying of concretes having a nominal

m£nt ratio of 0.636, to various independent variables

SO3 Loss APF Zn Rb SrO Pb Percent wt gain S.D.

-0.00403

(0.00080) -0.00433

(0.00077) -0.00463

(0.00103) -0.00325

(0.00128) -0.00449

(0.00081) -0.00468

(0.00078) -0.00454

(0.00104) -0.00424

(0.00127)

+0.00105

(0.00074) -0.00230

(0.00046) -0.00214

(0.00044) -0.00164

(0.00051) -0.00323

(0.00088) -0.00251

(0.00046) -0.00235

(0.00045) -0.00157

(0.00051) -0.00393

(0.00087)

+0.00000301

(0.00000053) +0.00000315

(0.00000051) +0.00000310

(0.00000058) +0.00000284

(0.00000100) +0.00000334

(0.00000054) +0.00000340

(0.00000052) +0.00000311

(0.00000060) +0.00000362

(0.00000099)

-0.0110

(0.0065) -0.0207

(0.0100) -0.0107

(0.0092)

-0.0109

(0.0064) -0.0213

(0.0101) -0.0092

(0.0086)

+0.3894

(0.1161) +0.2922

(0.1792) +0.3526

(0.1702)

+0.004.38 (0.00199) +0.00592

(0.00278) +0.00315

(0.00314)

-0.00.394

(0.00278) *- 0.00.345 (0.00372) -0.00591

(0.00439)

-0.0450

(0.0345) -0.0867

(0.0483) ^-0.0234

(0.0513)

+0.3461

(0.1162) +0.2940

(0.1819) +0.3070

(0.1631)

+0.00473

(0.00196) +0.00629

(0.00276) +0.00423

(0.00302)

-0.00432

(0.00275) -0.00369

(0.00378) -0.00644

(0.00415)

-0.0432

(0.0340) -0.0837

(0.0487) -0.0275

(0.0489)

0.003509

0.002857

0.002702

0.002475

0.002912

0.002807

0.002664

0.002490

0.002778

V in eq 5 resulte(i in a further significant re- duction in the S.D. value.

The use of major oxides with other commonly

determined variables in eq 6 resulted in a

highly significant reduction in the S.D. value.

It may be noted, however, that the coefficient

for Fe203 was negative whereas that for C4AF

in eqs 4 and 5 were positive. Neither was

highly significant ^. The additional use of the

trace elements in eq 7 resulted in a further

significant reduction in the S.D. value (see

table 10-44).

In equations for the "odds" and "evens" (eqs

5A, 5B, 7A and 7B) there were instances where

the coef./s.d. ratios for C3S, FesOs, K2O, MgO,

air content, Mn, P, V, and Ni were less than

1 in one or both, of the pairs of equations for

the smaller groups of cements.

A corresponding series of equations for NAE

cements is presented in table 10-17. The coefficients of the various independent variables

and the reduction in variance resulting from

the use of additional independent variables were in reasonable agreement with those presented in the previous table 10-16 where the

AE cements were included.

Using the coefficients of the independent

variables from eq 5 of table 10-17 and the

approximate ranges of these variables, calculated contributions to the expansion, and the

ranges of such contributions were determined.

As indicated in table 10-18, increases in C3A,

C4AF, MgO, KoO, fineness, and Mn were associated with increases in the expansion values.

Increases in SO3 and Loss were associated with

decreases in the expansion values. Differences

in C3A, fineness, and SO3 had the largest cal-

' The C4AF value was computed as a constant times the FezOa

in accordance with specification requirements.

culated effect on differences of expansion values

obtained.

6.4. Residual Shrinkage or Difference between

the Percentage Shrinkage During Drying

and the Percentage Expansion with Subsequent Rewetting

a. Residual Shrinkage of Series O Concretes made with

a water/cement Ratio of 0.635 (ODSX)

The frequency distributions of the residual

shrinkage, defined as the difference between the

shrinkage during air drying for 56 days and

the expansion during the subsequent water

storage for 28 days, of the Series 0 concretes are presented in table 10-19. There was a fairly

broad range of values and an overlapping of

the values obtained with the different types of

cement.

Equations presenting the variables associated with the residual-shrinkage values for

AE I- NAE cements are presented in table

10-20. The use of commonly determined variables in eq 1 resulted in a highly significant

reduction in the S.D. value, and the additional use of the trace elements SrO, Li, and Rb in

eq 2 resulted in a further highly significant re- duction in the S.D. value. The S.D. value of

eq 2 was higher than that obtained when the

shrinkage values were used as independent

variables as in eq 3. The use of additional independent variables having coef./s.d. ratios

greater than 1 in eq 4 caused a significant re- duction in the S.D. value (see table 10-44).

The coef./s.d. ratios of C4AF, APF, and Loss were less than 1 when included with the other

variables in eq 4, but the coef./s.d. ratio for

MgO was greater than 1. Except for SrO and

51
Table 10-16. Coefficients for equations for AE-\-NAE cements relating AEXP, theperceni a nominal 5}^<z bags of cement per cubic yard with

FjQUiiljion Note Const. CiA CsS CiAF

nik J AEXP = +0.0237

s.d. AEXP

(0.0076) = +0.0163

s.d. AEXP

= (U.UU2U)

(') = +0.0166 +0.000485 *+ 0.0000389 +0.000236

s.d. = (U.UUo2) = +0.0107

(.U . UUUJlUi>; +0.000710

(.U. UUUlOU;

(') AEXP -0.0000542 + 0.000366 +0 00174

s.d. = (0.0030) (,U. UUUlUi; (U . UUUUoyoJ t,U . UUUioUJ (0 00130)

(') AEXP = +0.0085 +0.000725 -0.0000440 +0.000344 4-0 00260

s.d. = (0.0032) (U. UUUilUJ ^U-UUUUoCS/ } (,U. UUUloi; (0 00130)

(') AEXP (odd) = +0.0107 +0.000658 *- 0.0000482 + 0.000366 -1-0 00479

s.d. = (0.0042) \\) . 1)0014:^; iC\ f\f\nf\AQCi\ /A AAA^'7A^ t,U. UUUl (0 00167) 5B (') AEXP (even) = +0.00d9 -\-\} . UUU/ LI ^ — U . UUUU

oo 1 A AAAOQV *+0 00055

s.d. = (0.0050) (0.000172) (0.0000662) (0.000208) (0 00217) CaO =====

AI2O3 Fe203

6 () AEXP = +0.0551 -0.000682 +0.00182 -0.000451 +0 00141

s.d. = (0.0167) (,U . UUUJ4D; (,U. UUU-600 (0 00131)

(') AEXP = +0.0483 -0.000606 +0.00186 -0.000521 +0 00237

s.d. = (0.0167) (0 . UUUz4o; (,U . UUU/y; vU.UUUool; (0 00132) 7A (') AEXP (odd) = +0.0412 -0.000475 +0.00169 *- 0.000213 +0 00451

s.d. = (0.0226) (0.000335) (0.00037) (0.000457) (0 00172) 7R (') AEXP (even) = +0.0493 -0.000629 +0.00185 -0.000932 *+0 00077

s.d. = (0.0257) (0.000382) (0.00045) (0.000552) (0 00209)

' 171 cements; Avg = 0.02100 percent; S.D. = 0.003823. 2 86 cements. ^ 85 cements. * Coef./s.d. ratio less than 1.

Table 10-17. Coefficients for equations for NAE cements relating AEXP, the percentage nominal 5} 2 bags of cement per cubic yard with a

Equation Note Const. CsA CiAF

1..

2..

3..

4..

5..

5A.

5B.

6..

7..

7A

7B

{>)

(')

(•)

(')

(')

(2)

(')

(')

(')

AEXP

s.d. AEXP

s.d. AEXP

s.d. AEXP

s.d. AEXP

s.d. AEXP (odd)

s.d. AEXP (even)

s.d.

AEXP

s.d. AEXP

s.d. AEXP (odd)

s.d. AEXP (even)

s.d.

+0.0073

: (0.0101) +0.0159

= (0.0020) +0.0165

= (0.0033)

= +0.0122

= (0.0031)

= +0.0094

= (0.0032) +0.0152

= (0.0040)

= +0.0024

= (0.0052)

: +0.0606

= (0.0188)

= +0.0533

= (0.0168)

= +0.0582

= (0.0206)

= +0.0357

= (0.0290)

+0.000498

(0.000107) +0.000722

(0.000102) +0.000748

(0.000111) +0.000797

(0.000152) +0.000738

(0.000705)

-0.0000443

(0.0000435) -0.0000645

(0.0000401) -0.0000504

(0,0000390) -0.0001181

(0.0000452) *+0. 0000484

(0.0000706)

+0.000254

(0.000154) +0.000335

(0.000130) +0.000329

(0.000130) +0.000303

(0.000169) +0.000365

(0.000184) CaO AI2O3 FejOi -0.000749

(0.000247) -0.000672

(0.000248) -0.000717

(0.000303) -0.000447

(0.000434)

+0.00186

(0.00027) +0.00193

(0.00029) +0.00209

(0.00040) +0.00195

(0.00045)

-0.000578

(0.000358) -0.000626

(0.000348) -0.000595

(0.000464) -0.000604

(0.000524)

i 159 cements; Avg = 0.02085 percent; S.D. = 0.003821. 2 80 cements. I cements. * Coef./s.d. ratio less than 1.

52
age expansion after 28 days moist storage following 56 days of drying of concretes having a 5 :k 1 in. slump, to various independent variables

S03 MgO Loss APF Air content Mn P V Ni W/C Percent

\vt gain S.D.

*-0. 00428

(0.01188) 0.003832

+ 0.00184

(0.00075) 0.003767

0.003611

-0.00494

(0.00091) -0.00548

(0.00090) -0.00582

(0.00128) -0.00453

(0.00132)

-0.00522

(0.00091) -0.00572

(0.00091) -0.00596

(0.00129) -0.00479

(0.00132)

+0.000436

(0.000217) +0.000428

(0.000222) *+0. 000257

(0.000304) +0.000555

(0.000342)

-0.00252

(0.00050) -0.00250

(0.00049) -0.00285

(0.00070) -0.00204

(0.00071)

-0.00296

(0.00051) -0.00290

(0.00050) -0.00316

(0.00074) -0.00246

(0.00071)

+0.00000393

(0.00000062) +0.00000431

(0.00000062) +0.00000386

(0.00000086) + 0.00000429

(0.00000095)

+ 0.00000398

(0.00000059) + 0.00000435

(0.00000060) +0.00000381

(0.00000083) + 0.00000450

(0.00000091)

+0.000214

(0.000117) +0.000208

(0.000114) +0.000316

(0.000163)

* +0. 000114

(0.000170)

+0.000206

(0.000117) + 0.000202

(0.000114) +0.000314

(0.000162) *+0. 000097

(0.000168)

0.003011

+ 0.00418

(0.00195) *+ 0.00043

(0.00310) + 0.00615

(0.00278)

+0.00284

(0.00215) + 0.00510

(0.00331)

* +0. 00051

(0.00303)

+0.0237

(0.0154) *+0.0065

(0.0196) +0.0533

(0.0260)

+0.1149

(0.0830 +0.2155

(0.1172) *+ 0.0043

(0. 1353)

0.002916

0.002668

0.003125

0.002998 +0.00425

(0.00194) *+0. 00031

(0.00307) +0.00635

(0.00274)

+0.00278

(0.00213) +0.00505

(0.00328) *+0. 00043

(0.00302)

+ 0.0229

(0.0151) *+0.007]

(0.0185) +0.0531

(0.0258)

+0.1098

(0.0828) +0.2149

(0.1164) *-0.0073

(0.1346)

0 . 002909

0.002650

0.003110

xpansion after 28 days moist storage following 66 days of drying of concretes having a 6 ± 1 in. slump, to various independent variables

S03 MgO Loss APF Mn P V Ni W/C

Percent wt gain S.D.

+0.02111

(0.01583) 0.003811

+ 0.00190

(0.00077) 0.003760

0.003597

-0.00523

(0.00091) -0.00588

(0.00090) -0.00765

(0.00121) -0.00466

(0.00140)

-0.00553

(0.00091) -0.00615

(0.00091) -0.00765

(0.00121) -0.00471

(0.00144)

+ 0.000438

(0.000220) +0.000446

(0.000222)

* +0. 000119

(0.000285) +0.000597

(0.000356)

-0.00243

(0.00050) -0.00240

(0.00049) -0.00225

(0.00065) -0.00240

(0.00080)

-0.00290

(0.00051) -0.00282

(0.00050) -0.00268

(0.00070) -0.00269

(0.00078)

+ 0.00000393

(0.00000063) +0.00000434

(0.00000062) +0.00000467

(O.O00OOC81) +0.00000407

(0.00000097)

+0.00000395

(0.00000059) + 0.00000438

(0.00000060) +0.00000435

(0.00000079) +0.00000442

(0.00000095)

0.002978

+ 0.00413

(0.00201) *- 0.00103

(0.00288) +0.00707

(0.00294)

+0.00272

(0.00212) +0.00396

(0.00315) *- 0.00057

(0.00308)

+0.0297

(0.0152) *-0.0007

(0.0180) +0.0715

(0.0262)

+0.1096

(0.0828) +0.2475

(0.1142) *-0.0023

(0.1,301)

0.002861

0.002572

0.003032

0.002959

+0.00415

(0.00200) *-0. 00131

(0.0029) +0.00703

(0.00296)

+0.00262

(0.00211) +0.00388

(0.00318) *- 0.00054

(0.00310)

+0.0293

(0.0149)

* +0.0053

(0.0177) +0.0689

(0.0262)

+0.1028

(0.0824) +0.2334

(0. 1151) *-0.0258

(0.1302)

0.002848

0.002595

0.003050

53
Table 10-18. Calculated contributions to the percentage expansion after 28 days in water following 66 days air-drying of concretes having a nominal 514. bags of cement per cubic yard

and a slump of 6 ± 1-in., and the calculated ranges of such

contributions (AEXP)

T H

\ til lOiL'lCo

Range of variables

(percent)

Coefficients from eq (5) table 10-17

Calculated contri- butions to AEXP

Calculat- ed ranges

of contri- butions

to AEXP

Const. = +0.0094 CsA 0 to 15 +0.000748 0 to +0.0112 0.0112 C3S** 20 to 60 — 0.0000504 -0.0010 to -0.0033 0.0023 CiAF 4 to 17 +0.000329 +0.0013 to +0.0056 0.0043 K2O 0 to 1.1 +0.00270 0 to +0.0030 0.0030 SO3 1.2 to 3.0 -0.00588 -0.0071 to -0.0176 0.0105 MgO 0 to 5.0 +0.000446 0 to +0.0022 0.0022 Loss 0.3 to 3.3 -0.00240 -0.0007 to -0.0079 0.0072 APF *2500 to 5500 + 0.00000434 -1-0.0108 to +0.0239 0.0131 Mn 0 to 1.0 -4-0.00413 0 to +0.0041 0.0041 p** 0 to 0.5 +0.00272 0 to +0.0014 0.0014 V** 0 to 0.1 + 0.0297 0 to +0.0030 0.0030 Ni** 0 to 0.02 +0.1096 0 to +0.0021 0.0021

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

Rb, the coefficients of none of the added independent variables were highly significant. In

eqs 2A and 2B, Na20, air content, and Li had

coef./s.d. ratios less than 1 in one or the other

of the smaller groups of cements. In eqs 4A and

4B, for the "odds" and "evens", NagO, C3A/

S0,3, air content, Li, and MgO had coef./s.d.

ratios less than 1. A corresponding series of equations for the

NAE cements is presented in table 10-21. As

in the previous table, the residual shrinkage

appeared highly related to the initial shrinkage

(see eq 3). Other additional independent variables such as SrO and Rb appeared to have

highly significant effects as indicated in eq 4. If the relationship of the difference between the

shrinkage and expansion is computed only with

the chemical composition and fineness of the

cement and the air content of the concrete as

Table 10-19. Frequency distribution of cements with respect to difference between the shrinkage and subsequent expansion of concrete of nominal 5]/^ bags of cement per cubic yard made with a water-cement ratio of 0.635 (ODSX)

Percentage shrin kage minus percentage expansion

-0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 Type cement to to to to to to to to to to to to to to Total

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026

Number of cements

I 1 1 3 5 14 16 19 13 5 1 1 1 1 1 82 lA 16

1 1 3 2 8

11 2 4 10 14 16 7 5 4 68 IIA 1 1 2

III... 3 3 3 4 6 1 20

IIIA 1 1 1 3

IV, V 2 4 3 3 3 15

Total 1 3 7 21 28 37 34 27 19 7 1 1 1 1 198

independent variables as in eq 2, a higher S.D.

value is obtained.

Calculated contributions and ranges of contributions to the residual shrinkage based on

eq 2, table 10-21, are given in table 10-22. In- creases in C4AF, CsA/SOa, fineness, and SrO

appear to be associated with increases in the

residual-shrinkage values. Increases of Na20,

loss on ignition, and Rb were associated with a

decrease in the residual-shrinkage values.

b. Residual Shrinkage of Series A Concretes made having a Slump of 5 ± 1 in. (ADSX)

The frequency distribution of the cements

with respect to the residual shrinkage of specimens made of Series A concretes is presented

in table 10-23. There was a fairly broad distribution of values, and an overlapping of the

values for the cements of the different types.

A series of equations is presented in table

10-24 to indicate the variables associated with

the values for the residual shrinkage of the

Series A concretes made of AE + NAE ce- ments. A corresponding series of equations for

the NAE cements is presented in table 10-25.

The independent variables associated with the

shrinkage-expansion differences for the specimens made of Series A concretes and those previously reported in tables 10-20 and 10-21

made of Series 0 concretes are in reasonable

agreement as are the coefficients of these variables. The differences between shrinkage and

expansion were significantly associated with

the magnitude of the shrinkage as indicated in

eq 3 of the two tables (see also table 10-44).

The additional use of commonly determined

variables in eq 4, or those with trace elements

in eq 5, resulted in significantly lower S.D. values. The use of commonly determined variables

in eq 1 or those with trace elements in eq 2,

but not including the shrinkage as an independent variable, each resulted in significant re- ductions in the S.D. values, but these values were higher than in eqs 3, 4 and 5 where the

shrinkage was also included as an independent

variable.

Calculated contributions and ranges of contributions of the variables of eq 2, table 10-25,

54
COCO wco

05 05 Ci COOO CJO

TP

O U50 oo oo oo oo

Oi CO doI ^

as ot~

CO

CO doI ^

CO CO

CD

OSX rtO doI '~'

a o

•oo

00 —I o^

ddI ~" oo ^ CO —I o oo

dd

QOtJH oo

dd

(NCJi

1-1 •gi OO

oo oo

<oco

CO o ooI ^ oo

NOoo

dd oo

ton" coo oo

oooooodd+^

-HOO «ooooo

dd+^

oo oo

dd

oo

oo

CD ''i^ CO (N ^ <>i OOoo

oo oo

-IO ooOO

dd

Oioo

dd

(NCO

r-lO OOoo

to o wco oooodd+^

oo oo

tD (N OOooddI

ID

CO <N M CO OOooddI ^

oo

oo

dd+ -

oodd+-'oo

dd

ID

M OOooOO

i-icD CO CD

(N ^ OOOOOO

OOO CO

CD ^ r-«

r-t C^ IN OO QOOO oo OO

oo OO OOI ^

OC3So OOO

00 »0 1-H CD —""t 0-*

CO lO --H oo oo

00CO'*

OS CD oo

(N -H CO d CO t-H CO oo -lO ooI ^ ooI ^

ool

C^l CO 00oooo oo

oo

oo

ooI ^ oo

oooooo

(NCO ooo oo oo

CO CO oooo

oo ooI ^

00 >o oco

CD CO ool^O

iD<N

CO lO 00 * oo

CD

O TJH CO OOoo

e<ioo coo

CD ^ oooo

ooI ^u u O (O

ooI ^u u o ^

ooI ^

II II 1

00Otj" O CO

ooI ^u a

O-d O CO

ooI ^

II II X

O-o" O 0!

ooI ^

OiO^ 00 ID C^QO oo OiCO t^co oo oo oo oo

oo

O CO ^ oo ooooI

coco

lO CO

Ok ^ ooooI ^

ooI

CD ID lO »0 to

CD --^ CO 00 •* ^ oo oo oo oo oo oo

oo oo oo

IIua IIa II

a-6 O-d O ai Ok

CO 5

e.5

to

-« ^

>: cu I s

to

¥

J §

1^2 II %9

i-2 ^ CO

S5

O--00 * CO lOO

•* oo

>oO

—.

»o o 3 ID Oco 0 00 o-< oo oo oo oo

ooI ^ * CD 1^

CO CO 1^ o Ol O Ol CN

CI CI dd dd

05

CIiO 00

CD CO CO CO coco OC33

00 CO OJ (N ooI ^ oo oo I ^ I -

oo

dd

oo oo

dd dd

lOt^ O "O c^o OOoo

NkO

00 to -HO ooOO

Tt'O oi»o

iO 05 CO C^O i-^O OO oo oo ooI ooI ^ oo oo

NCD CIO c o OOoo

COO

00 CD — o oo

C^ TJH OS O CO

d -HO oo oo OOoo oo CO oo

oo oo oo oo

OOO

co«

00 CO oooo

050 iOX

CD CO oo

OOrt -HO

-HUO ON OOCD CDIO oo oo

ooI " ooI ^ oo oo I ^ I

CO -H CI cs oooo

OCO OiOi -ho oo oooo

oo oo oo oo

ooCOoo

CJJ CO X X-H COoo

-HW dCO O* CI CD CJ CO CO oo OO oo oo

ooI ^ ooI 

oo oo I I ^

oo

O-H

-H oooooo

XCO t^Cl coco C0Q3

rj- (N * -H oo oo oo oo

oo oo oo oo

ooI

1^

X CI x-* x»o

CI

N -H CI oo oo oo oo

dd dd I ""^ I

CI

CI lO coo

CO 1-1

»0 CO Ol o 05 »0 ID CD

CO -H CO -H ooI o oo oo

-HCD XCD oo

ddI

CC -H CIO O-H ddI

Olo

co»o XCI oooo

t^iO t^CI XX "O d CO CO -HO oo oo oo oo

Ol-H XXCO CI oooocox 0-* X 05

CO CO oo oo

oo oo oo I I

ooooC o * 0> XX

-H CI -H oo oooo

ooI ^ 00 oo 1 I

CO -H lO * d -H

c_

O oo

CO

d -H -H ^05 Ol d

CO -H -H oo oo oo oo oo I \^

XOi

<3a CO d CO oo

t^co O d

dCO COoo

dX o: iO

O CO -H CO trio -H t3< oo OO

O CD 05

dX .-I -H d CO Oi

CO -H -H TT -H oo oo OO oo oo ooIu a

toO-d O £

ooI ^u u

too-d o o;

ooIa u ooI ^u a oo oo a a a a O <i m

(-1-1 O ;

to to O-d tl-d On' O ID

ooIa u

g1

-H

d

55
Table 10-22. Calculated contributions to the percentage shrink- age after 56 days drying minus the percentage expansion after 28 days in water of concretes having a nominal .5 '2 bags of cement per cubic yard and a water-cement ratio of 0.635, and

the calculated ranges of such contributions (ODSX =OSHR — OEXP)

Inde- pendentRantie of variables

(percent)

Coefficients from eci (2) table 10-21

Calculated contri- butions to ODSX

Calculat- ed ranges

of contri- butions

to ODSX

- Const. = -0.00207 CAF 4 to 17 -f 0.000440 -1-0.0018 to 4-0.0074 0.0056 Na50 0 to 0.75 -0.00489 0 to -0.0037 0.0037 C3A/SO3. 0.4 to 10.1 -1-0.00096 +0.0004 to -1-0.0097 0.0093

Air con- 0 to 10 -0.000659 0 to -0.0066 0.0066

tent.** APF *2500 to 5500 -1-0.00000183 -fO.0046 to +0.0101 0.0055 Loss 0.:} to 3.3 -0.00182 -0.0005 to -O.OOfiO 0.0055 SrO 0 to 0.4 4-0.0113 0 to +0.0045 0.0045

Li** 0 to 0.02 -0.1529 0 to -0.0030 0.0030 Rb 0 to 0.01 -0.3841 0 to -0.0038 0.0038

*cmVg.

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

to the residual-shrinkage values are presented

in table 10-26. Increases in C4AF, C3A/SO3,

fineness, and possibly SrO were associated with

greater residual shrinkage. Increases in Na20,

loss on ignition, and Li were associated with

decreases in the residual shrinkage. Of these,

differences in C4AF, C3A/SO3, and fineness had

the greatest calculated effect on the ranges of

the values for residual shrinkage. The air-con- tent and Rb, though of doubtful significance in

eq 2 of table 10-25, may possibly be significant

in eq 2 of table 10-24 where the AE cements were included.

Table 10-23. Frequency distribution of cements with respect to difference between the shrinkage and subsequent expansion of nominal

5]/2 bags of cement per cubic yard concretes with a 5 ± 1 in. clump (ADSX)

Percentage shrinkage minus percentage expansion

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 Type cement to to to to to to to to to to to to Total

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024

Number of cements

I 2 5 10 11

19

13

1 18

2

115

17 12

33

4

15

1

15

2 1 78

866

220

315

I A 1 II 1 6 8 11 IIA

III 3 3 8 5 IIIA 1 1 IV, V 1 1 4 2 2 Total 3 12 22 28 41 38 24 12 8 1 2 1 192

Table 10-24. Coefficients for equations for AE-\-NAE cements relating the difference he days loater storage {ADSX = ASHR-AEXP) of concretes having a nominal 6Y> bags

Equation Note Const. CiAF NazO C3A/SO3

1...

2...

2A.

2B.

3..

5...

5A.

5B.

(')

(')

(»)

(')

(')

(')

(')

(^)

(')

ADSX

s.d. ADSX

s.d. ADSX (odd) = s.d. ADSX (even) = s.d. ADSX

s.d. ADSX

s.d. ADSX

s.d. ADSX (odd) = s.d. ADSX (even) =

s.d.

-0.00673

(0.00318)

: -0.00519

(0.00304) -0.00423

(0.00466)

^ -0.00545

(0.00436) -0.00573

(0.00110) -0.00798

^ (0.00187) -0.00729

' (0.00184) -0.00708

(0.00279) -0.00742

(0.00254)

+0.000539 -0.00364 +0.00106

(0.000142) (0.00161) (0.00020) +0.000552 -0.00402 +0.00080

(0.000136) (0.00176) (0.00020) +0.000498 -0.00399 +0.00086

(0.000199) (0.00260) (0.00031) +0.000560 -0.00412 -0.00071

(0.000200) (0.00253) (0.00031)

+0.000098

(0.000088) +0.000175

(0.000086) *+0. 000106

(0.000125) +0.000212

(0.000123)

> 171 cements; Avg = 0.00907; S.D. = 0.00384. 2 ge cements. ' 85 cements. * Coef./s.d. ratio less than 1.

56
in one or the other or both of the equations for

these smaller groups of cements.

A similar series of equations relating the

expansion/shrinkage ratios of concretes made

of the NAE cements to various independent

variables is presented in table 10-29. The independent variables associated with the differ- ences in the ratios, their probable significance,

and the reduction in variance resulting from

their use in the multivariable equations were

in reasonable agreement with those of the preceding table 10-28 where the AE cements were

included.

Using the coefficients of the independent

variables of eq 2, table 10-29, and their ranges

of values, computations were made of the cal- culated contributions to the expansion/shrinkage ratio, as well as the calculated ranges of

these contributions. These calculated values are presented in table 10-30. Increases in NaoO, Li,

and Rb were associated with increases of the

expansion/shrinkage ratio. Increase in SrO as- sociated with a decrease in the ratio, whereas

C4AF, MgO, and Ba had coef./s.d. ratios of

doubtful significance.

b. Ratio of Expansion Divided by the Shrinkage of Concretes made having a Slump of 5 ± 1 in (AREX = AEXP/ASHR)

The frequency distribution of the cements

with respect to the expansion/shrinkage ratios

of Series A concretes is presented in table

10-31. The range of values for the ratio was

rather large and there was an overlapping of

the values of the cements of the different types.

Equations relating the expansion/shrinkage

ratio of the Series A concrete specimens made

of AE + NAE are presented in table 10-32. No

relationship was found between the ratio and

the water/cement ratio used in preparing the

tween the percentage shrinkage after 56 days drying and the percentage expansion after 28

of cement per cubic yard and a slump of 5 ± 1 in., to various independent variables

Air content APF Loss MgO SrO Li Mn Rb ASHR S.D.

+0.000338

(0.000129) +0.000272

(0.000122) + 0.000299

(0.000165) +0.000303

(0.000196)

+0.00000237

(0.00000059) +0.00000165

(0.00000056) +0.00000185

(0.00000094) +0.00000216

(0.00000075)

-0.00186

(0.00055) -0.00165

(0.00052) -0.00146

(0.00092) -0.00203

(0.00073)

0.00344 +0.0108

(0.0031) +0.0094

(0.0045) +0.0122

(0.0048)

-0. 1714

(0.0822) -0.2033

(0.1179) -0.1410

(0.1255)

-0.00274

(0.00208) -0.00662

(0.00285)

* +0. 00191

(0.00328)

-0.2812

(0.1337) -0.2497

(0.1719) -0.3311

(0.2280)

0.00323

0.00318

0.00340

+0.4933

(0.0360) +0.5066

(0.0351) +0.4705

(0.0364) + 0.4568

(0.0544) +0.4947

(0.0505)

0.00265

-0.000512

(0.000169) -0.000370

(0.000169) -0.000329

(0.000250) -0.000352

(0.000245)

0.00257

+0.0047

(0.0023) + 0.0051

(0.0032) +0.0034

(0.0033)

-0. 1459

(0.0573) -0. 1824

(0.0828) -0.0965

(0.0837)

-0.00305

(0.00162) -0.00640

(0.00224)

* +0.00027

(0.00241)

-0.2592

(0.1005) -0.2660

(0. 1284) -0.2634

(0.1667)

0.00246

0.00241

0.00251

! 6.5. Ratio of Percentage Expansion Divided by

I the Percentage Shrinkage

a. Ratio of Expansion Divided by the Shrinkage of Series O Concretes Made with a Water/Cement Ratio

of 0.635 (OREX = OEXP/OSHR)

The frequency distribution of the cements

with respect to the ratio of the expansion di- vided by the shrinkage of Series 0 concretes of

AE + NAE cements is presented in table 10-

27. Although there was a considerable range

of values for the ratio, and an overlapping

] of the values for the cements of the different

types, the averages of the ratios of the airentraining cements were close to the averages

of the NAE cements.

I Equations relating the expansion-shrinkage

'i ratio of Series 0 concretes to various indepeni dent variables are presented in table 10-28.

' Equation 1 indicates that this ratio is significantly related to the shrinkage of the speci-

! mens when dried in laboratory air for 56 days

(see table 10-44). Use of the independent variables associated with the chemical composition

of the cements, as in eq 2, produced an equivaI lent S.D. value. Using the chemical-composition variables and the shrinkage in eq 3 re- sulted in a significant reduction in the S.D.

value (see table 10-44). Equations 4, 6, and 7,

I calculated with C3A, Fe203, and AI2O3 respec-

\ tively in place of the C4AF of eq 3, resulted in

S.D. values which were close to that obtained

in eq 3.

j In eqs 2A and 2B for the "odds" and "evens"

I there were instances where the coef./s.d. ratios

of C4AF, and MgO were less than 1. In equations using the "odds" and "evens" of the equations 3, 4, 5, 6, and 7, not presented in the

table, C4AF, FeoOs, C3A, AI2O3, NasO, MgO, Li,

and Ba, all had coef./s.d. ratios less than one

57
Table 10-25. Coefficients for equations for NAE cements relating the difference between

water storage {ADSX = ASHR-AEXP) of concretes having anominal 5}/2 bags of ce

Equation Note Const. C4AF Na20 C3A/SO3 SO3

1 (>)

(')

{')

(«)

(')

(')

()

ADSX =-0.00486

s.d. = (0.00319) ADSX =-0.00424

s.d. = (0.00310) ADSX (odd) == -0.00514

s.d. = (0.00524) ADSX (even) = -0.00272

s.d. = (0.00399) ADSX =-0.00547

s.d. = (0.00114) ADSX =-0.00735

s.d. = (0.00199) ADSX = -0.00760

s.d. = (0.00193) ADSX (odd) = -0.00969

s.d. = (0.00285) ADSX (even) = -0.00682

s.d. = (0.00282)

+0.00051

(0.00014) +0.00054

(0.00014) 4-0 ^KJ . OOflfiR UvUJO

+0.00046

(0.00018)

-0.00365

(0.00159) -0.00396

(0.00177)

(0 00987^ — n 00346

(0.00239)

+0.00098

(0.00020) + 0.00078

(0.00021)

-1-0 000^^1 (n 000^4^

(0.00028)

o

OA

OH

+0.000119

(0.000089) +0.000199

(0.000087) +0.000318

(0.000146) +0.000146

(0.000108)

+0.00116

(0.00059) +0.00094

(0.00059) +0.00166

(0.00085) *+0. 00084

1 (0.00084)

e

5A

5B

« 159 cements; Avg = 0.00886; S.D. = 0.00376. 2 80 cements. ' 79 cements. * Coef./s.d. ratio less than 1.

concretes, see eq 1. Using commonly determined

variables in eq 2 resulted in a significant re- duction in the S.D. value, but in eq 4 the indication of reduction was significant at the 5- percent probability level (see table 10-44). The

additional use of the trace elements Li, SrO,

Mn, Rb, Zn, and Ba in eqs 3 and 5 resulted in

significant reductions in the S.D. values al- though none of the individual variables except

SrO had high coef./s.d. ratios (see table 10-

44). The coef./s.d. ratios of C3A, C2S, Wagn,

Mn, Zn, and Ba were less than 1 in one or the

other of the pairs of equations for the "odds"

and "evens", eqs 3A, 3B, or 5A, 5B. Equation 6

gives a significant indication that the expansion/shrinkage ratio was associated with the

shrinkage values of the concretes. The use of

other independent variables in addition to ASHR in eq 7 resulted in a further significant

reduction in the S.D. value (see table 10-44).

Table 10-26. Calculated contributions to the percentage shrink- age after 56 days drying minus the percentage expansion after 28 days in water of concretes having a nominal 5^ 2 bags of cement per cubic yard and a slump of 5 ± 1 in., and the cal- culated ranges of such contributions {ADSX = ASHR — AEXP)

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (2) table 10-25

Calculated contri- butions to ADSX

Calculat- ed ranges

of contri- butions

to ADSX

Const. = -0.00424 C.AF 4 to 17 +0.00054 +0.0022 to +0.0092 0.0070 NasO 0 to 0.75 -0.00396 0 to -0.0030 0.0030 CaA/SOj. 0.4 to ] 0.1 +0.00078 +0.0003 to +0.0079 0.0076 Air con- 0 to 13 -0.000336 0 to -0.0044 0.0044

tent.** APF *2500 to 5500 +0.00000218 +0.0054 to +0.0120 0.0066 Loss 0.3 to 3.3 -0.00188 -0.0006 to -0.0062 0.0056 SrO 0 to 0.4 +0.0089 0 to +0.0036 0.0036

Li 0 to 0.02 -0.1431 0 to - 0.0029 0.0029 Mn** 0 to 1.0 -0.00294 0 to -0.0029 0.0029 Rb** 0 to 0.01 -0.1861 0 to -0.0019 0.0019

cmVg.

^Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

58
the percentage shrinkage after 56 days drying and the percentage expansion after 28 days ment per cubic yard and a slump of 6 ± 1 in., to various independent variables

Air content APF

* Loss MgO SiO Li Mn Rb ASHR S.D.

-0.000423

(0.000308) -0.000336

(0.000309) -0.000553

(0.000541) *-0. 000173

(0.000402)

+0.00000243

(0.00000059) +0.00000218

(0.00000057) +0.00000269

(0.00000103) +0.00000173

(0.00000069)

-0.00214

(0.00055) -0.00188

(0.00053) -0.00211

(0.00094) -0.00178

(0.00066)

0.00333

+0.0089

(0.0032) +0.0106

(0.0051) +0.0067

(0.0044)

-0.1431

(0.0834) *-0.1217

(0.1292) -0.1754

(0.1221)

-0.00294

(0.00213) -0.00.357

(0.00290) -0.00.389

(0.00378)

-0.1861

(0.1.375) *-0.1142

(0.2071) -0.3084

(0.2034)

0.00320

0.00352

0.00301

+0.4834

(0.0378) +0.4925

(0.0368)

(0.0382) +0.4786

(0.0562) +0.4767

(0.0543)

0.00264

-0.000321

(0.000233) -0.000534

(0.000172) — u . uuuoyy

(0.000174) *+ 0.000092

(0.000286) -0.000647

(0.000216)

0.00254

(0.0023) +0.0051

(0.0036) *+0.0016

(0.0031)

— U . 11 /

O

(0.0573) -0.1937

(0.0843) -0.1108

(0.0802)

— U . UUoiO

(0.00166) -0.00557

(0.00228) *+0.00046

(0.00282)

— 0 . 2462

(0.1024) -0.3112

(0.1477) -0.2503

(0.1488)

\J . UUJ^O

0.00267

0.00223

Table 10-27. Frequency distribution of cements with respect to ratio, percentage expansion divided by percentage shrinkage, for con

cretes having a nominal 5]4 bags of cement per cubic yard and a water-cement ratio of 0.636 (OREX =OEXP/OSHR)

Type cement

Ratio

Total

0.35

to 0.40

0.40

to 0.45

0.45

to 0.50

0.50

to 0.55

0.55

to 0.60

0.60

to 0.65

0.65

to 0.70

0.70

to 0.75

0.75

to 0.80

0.80

to 0.85

0.85

to 0.90

0.90

to 0.95

0.95

to

1.00

1.00 and

over

Number of cements

I 3 1 6

2

9

15

312

26

15

18 14

18

14

2

5

7 1 1 2 82

868

220

3

15

lA

II 2 18 7 3 3 1 IIA

III 1 4

12

4 1 4 IIIA 1 IV, V 2 3 2 1

Total 3 0 0 3 20 44 43 30 24 19 5 4 0 3 198
Tl^ CO COX

00

w1 ^ ^ CD CO ^ do

OCD

00 Ol -^CO do oo

r-ooI ^

OQO

CO

O

C^O dd ^ IN OS ^

CD -H ^~o dd

CO 00 oco

OS CO

CO r-i dd

OO rj< O d 1-1

^ao 00 COO (NCSl coo r^o OO oo

1> ^CD Of?

r}< CO Olio N CO 00^Tt^ CO rHO

O"*

(MCO o>o <NCO .-H CO (N CO (M CO ^ CO + + + + + + + +

CO o

CD 00

CO

O

CO

CO COCO

l-H 0 05

lO o 00

<M

O coo

OlO

SO GO COO

00 IC (N

O

O lO lO <MO ca O ooi OO oo ooI ^ ooI ^ ooI

00 lO

lO --I

rf^ CO

COCO 00 CO 00 l>OiTi* coco

05 1-t CO--! CO —1

"^ CO CD(N coco oco COM <C IM IN

00 CD OOOO

COW

CD CD CD 03 OOC OOiO

00 00 OOO o X CO i-H 00 0 CO lO

01 »o 00 o oo OO

CD

W

00 CD OOoo

t-CO TlHOl OCD --HiC 05 OS IC oo oo

oo oo oo oo oo oo oo

CDCOOi 00 Tj* oo

O 05 CO CO

lO

CO Tt^ IN Tt^ .-HO rHO

CO

CO Oi i-iO

CO TIH IN TlH OO OO OO oo oo oo

00 00 05TP oooo

dd

oo

05 03

Oioooo oooo

IN 00 COIN oo

ooI ^ oo oo oo

oo

OiOiOO ooddI

lOCO

lO CO

Oi o

coo

lOQO

Oi CO

CD

O

(NO 0-*

00 Oi Oi >—

00 TP CO ^

ooo ooo

CO "-I mo t-H »0 00 00 Cli X Oi

(3i CO 00

O It* coo ooo ooo oo oo oo oo oo oo oo oo

II 11 II 11 II II II II II

U II II 11 11 0 II II II

•a

"c T3 > o X X . X

XXX

XX

a

HwwwH

K " O c5 O

O toOd

O CD- o «;

•1

M « II

Oi.« •|« Si ;i

5^

gi^

.0 ISO

gi e

•S « «^

S~ Si ^ S

CO

O e CO s g S s H

1^n<

r^co

coci d -< I

CO 00

<J> o d IN * N dd

w o Oi CO COCO dd

TP CO O C>) OiOi

Tf IN dd+^

Oi CO

w

001 ooo

(NIN r^co I I

--I Oi Oi CO COlO coco '-O 1^0

tNIN ININ dd dd +^ +-'

0000 OiO

ININ

Tj^ IN dd

00 1~ 00s

IN CO

»0 Oi 10 o CD 10 10 W

-•O t^O

C4(N C<I(N 00 00

WOO

COb- Oco

—1 IN •00 oP.-IT|< Oi woo

cot-* CD>0

(NCO CO in CO in CO CO .-H CO (NCO COCO + + + + + + + +

CD

O COOi

CO

O

00c^rco -o 00 (MTf< CO 10 o lo CO 01 cooo woo

(NO coo

coo

CD Oi coo

I> CO(N o»o coo

CD

X -'01

<N

O CO

O

00I ^ 00I ^ 00 00 00 00I ^ 00 ^ Oi

COCT) OCO

COCO

Tjl CO

CD CO CO (N 00 CM (N (M 010

COO

OOCO COI>

CO CO CO

w

00(N r-((N CO <M CO r- CO CO N M CD IN COW

wo10

Oi CD 00

CD

Oi

w

CT- 0000

Oi 00

CO CD 001 woO O

00 Oi CO o^ 00 00

OiO

CO »o

c:ico 0000

OiCD

Oi

10 0000 00OS

00 00 00 00 00 00

>oo

CD CO CO 10 o-^ cow

CO

CO o

10 CO coo

woo wo 00 010

00

w

CO CO Tji wo wo

>no

CO CO cote wo 00 t^coTJiOO wt^

COTt* COTtI wo wo

00 00 00 00 00 00 00 00

0-* w 10 "OCO CO00

dd+^

o-*

CDQO wO00

dd+^

Oi CO oco

TJI CO o o 00

00 00

00 c^ OiO 00

coco O CO CD TP 0000

O »oOi

C^l CO 00

00I ^ 00I ^ 00

CD 00 COOi oS

coo

00 Oi 0000

00 00

CD Oi CD CO 010

COOi

Oico (DO

0(M

CO <M

CO to coo

CD

OCO OlO

I- o

00 10 cor-* 00 W -^Tj* 000 000

Oi CO O^O b-O

CO 01 Oi'-f

O (N Oi CO OJ lO coo 000 000 00

§1

00 00 00+^ +^ U II II II II II II II II li U II II II II II

-a

'c T30 X X

X

XXX

w

H

w 0 « 0 i/J 0 oi 0 m 0 m

60
Table 10-30. Calculated contributions to the ratio, percentage expansion after 28 days in water divided by percentage shrinkage after 66 days of drying, for concretes having a nominal

5Yi bags of cement per cubic yard and a water-cement ratio of 0.635, and the calculated ranges of such contributions (OREX

= OEXP/OSHR)

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (2) table 10-29

Calculatpd contri- butions to OREX

Calculat- ed ranges

of contri- butions

to OREX

Const. = -1-0.6935 CiAF**-- 4 to 17 -0.00409 -0.016 to -0.060 0.054 NasO 0 to 0.75 -1-0.1665 0 to -1-0.125 0. 3 25 MgO**._. 0 to 5.0 -1-0.00941 0 to +0.047 0.047

Li 0 to 0.02 + 6.0.34 0 to +0.121 0.121 SrO 0 to 0.4 -0..3667 0 to -0.147 0.147 Rb 0 to 0.01 -f 12.31 0 to +0.123 0.123 Ba** 0 to 0.2 -f 0.4293 0 to +0.086 0.086

Coefficient of doubtful significance as coef./s.d. ratio was less than 2,

A corresponding series of equations for the

NAE cements is presented in table 10-33 indicating the variables which were associated with

the expansion/shrinkage ratios of the Series A

concretes. The equations presented in table 10-

33 are in reasonable agreement with those

presented in the previous table 10-32 where the

AE cements were included in the calculated

multivariable equations, (see also table 10-44).

Using the independent variables of eq 3 of

table 10-33 and the ranges of these variables,

calculations were made of the calculated contributions and ranges of contributions to the ex- pansion/shrinkage ratios. The results of these

calculations are presented in table 10-34. The

coef./s.d. ratios of C3A, CoS, Rb, Zn, and Ba

were all less than 2 in eq 3 of table 10-33, and

Table 10—31. Frequency distribution of cements with respect to the ratio, percentage expansion divided by the percentage shrinkage

for concretes having a nominal 5Yi bags of cement per cubic yard and a slump of 6 ± 1 in. (AREX =AEXP/ASHR)

Type cement

Ratio

Total

0.40

to 0.45

0.45

to 0.50

0.50

to 0.55

0.55

to 0.60

0.60

to 0.65

065

to 0.70

0.70

to 0.75

0.75

to 0.80

0.80

to 0.85

0.85

to 0.90

0.90

to 0.95

0.95

to 1.00

Number of cements

I 3 22

2

2 133

9

15

1 19

16 10

2

6

12

8 4 3 2 78

866

2 20

3

15

lA

II 4 13

12

14

5 3 5 IIA in 1 3

14

10

14

1 1 IIIA

IV, V 2 1

Total 3 0 6 7 33 50 37 • 23 14 9 8 2 192

] of the other independent variables all but MgO

had coef./s.d. ratios between 2 and 3. MgO had

a coef./s.d. ratio of less than 1 in eq 3A for one

of the smaller groups of cements (the odds).

There is a significant indication then, than an

increase of the expansion/shrinkage ratio may

be associated with an increase in Na^O, MgO,

Li, and Mn. An increase in the expansion/

shrinkage ratio may possibly also be associated

with decreasing values for C4AF, fineness, and

SrO.

6.6. The ratio of the Residual Shrinkage after

Rewetting to the Initial Shrinkage (OREX

and AREX)

The frequency distributions of the cements

with respect to the ratio (OSHR-OEXP)/

OSHR and (ASHR-AEXP/ASHR are presented in tables 10-35 and 10-36 for the Series 0 and Series A concretes respectively. There was a considerable range of ratios in each of

the tables and an overlapping of the values for

the cements of different types.

Equations are presented in table 10-37 indicating the independent variables having a

coef./s.d. ratio greater than 1 which may be

associated with the (residual shrinkage divided by the shrinkage) ratios (OREX and

AREX) for both AE + NAE and the NAE

cements. In equations for OEXR, none of the

major potential compounds or major oxides had

coef./s.d. ratios greater than 1 when used in

multivariable equations with other independent

variables. None of the other independent variables in eqs 1 and 2 except NaoO and SrO had

coef./s.d. ratios greater than 3. Only SrO had

a coef./s.d. ratio greater than 3 in the two equations for the Series A concretes, eqs 3 and 4. As

indicated in table 10-44, there was a highly

significant reduction in variance with each of

the four equations of table 10-37.

The calculated contributions to the OEXR

ratio, and estimated ranges of these contributions, are presented in table 10-38 for the Series 0 concretes. Increases in SrO and possibly

Pb were associated with increases in the ratio.

Increases in NaoO, and possibly SO3, Li, and

Rb were associated with decreases in the ratio.

The effect of the variables MgO, Ba, V, and P

were of doubtful significance.

61
Table 10-32. Coefficients for equations for AE & NAE cements, relating the ratio, per

bags of cement per cubic yard and a slump of 6 ± 1 in. Specimens were moist cured for 2 weeks, then air dried

Equation

1...

2...

3...

3A.

3B.

4...

5...

5A.

5B.

6..

7...

Note

{')

(.')

(>)

(')

(»)

(')

(1)

(^)

(=)

(')

(1)

AREX

s.d. AREX

s.d. AREX

s.d. AREX (odd) = s.d. AREX (even) = s.d. AREX

s.d. AREX

s.d. AREX (odd) = s.d. AREX (even) = s.d. AREX

s.d. AREX

s.d.

Const.

= +0.729

(0.189)

= + 1.039

= (0.109)

= +0.924

= (0.108)

= +0.860

= (0.141)

= + 1.017

= (0.185)

= +0.757

= (0.067)

= +0.787

= (0.065)

= +0.700

= (0.096)

= +0.855

= (0.094)

= +0.899

= (0.036)

= +0.861

= (0.045)

CaA

-0.0115

(0.0032) -0.0046

(0.0036) -0.0074

(0.0047) *-0.0049

(0.0064)

C2S C4AF

-0.00161

(0.00115) -0.00180

(0.00109) *- 0.00098

(0.00129) -0.00280

(0.00217)

-0.00924

(0.00368) -0.00830

(0.00364) -0.00883

(0.00525) -0.00974

(0.00561)

0.00467

(0.00277)

1 170 cements; Avg = 0.7045; S.D. = 0.0941. 2 85 cements.

* Coef./s.d. ratio less than 1. ** Coef./s.d. ratio less than 1 in equations for "odds" and "evens".

Table 10-33. Coefficients for equations for NAE cements, relating the ratio, percentage cement per cubic yard and a slump of 5 ± 1 in to var

Specimens were moist cured for 2 weeks, then air dried

Equation Note Const. CjA CzS C.AF

1..

2..

3-

3A.

3B.

4..

5..

6A

5B

6..

7..

(>)

(')

(')

in

()

(')

(^)

i')

(')

(')

AREX

s.d. = +1

= (0 051

256) AREX

s.d. = + 1 = (0 024

110) AREX

s.d. = +0

= (0 928

110) AREX (odd)

s.d. =+1

= (0 108

170) AREX (even)

s.d. = +0

= (0 757

152) AREX

s.d. = +0

= (0 781

068) AREX

s.d. = +0

= (0 809

068) AREX (odd)

s.d. = +0

= (0 913

113) AREX (even)

s.d. = +0

= (0 723

083) AREX

s.d. = +0

= (0 895

038) AREX

s.d. = +0

= (0 860

046)

-0.0101

(0.0033) -0.0042

(0.0037) -0.0075

(0.0055) -0.0007

(0.0053)

-0.00127

(0.00117) -0.00154

(0.00112) -0.00186

(0.00159) *-0. 00102

(0.00177)

-0.0099

(0.0037) -0.0090

(0.0037) -0.0140

(0.0061) -0.0054

(0.0048)

-0.0054

(0.0028)

1 158 cements; Avg = 0.7077; S.D. =0.0942. 2 79 cements.

* Coef./s.d. ratio less than 1. ** Coef./s.d. ratio less than 1 in equations for "odds" and "evens".

62
centage expansion divided by the percentage shrinkage, for concretes having a nominal 614

to various independent variables {AREX = AEXP/ASHR)

for 8 weeks and then placed in water for 4 weeks.

NajO MgO WAGN Li SrO Mn Rb Zn Ba W/C ASHR S.D.

* — 0.0412

(0.2970) 0.0955

+0.0974

(0.0418) +0.0946

(0.0461) +0.1020

(0.0692) +0.0982

(0.0670) +0.0765

(0.0425) +0.0844

(0.0459) +0.0805

(0.0682) +0.0817

(0.0646)

+0.0174

(0.0058) +0.0163

(0.0059) +0.0156

(0.0082) +0.0150

(0.0098) +0.0148

(0.0060) +0.0158

(0.0059) +0.0162

(0.0082) +0.0113

(0.0093)

-0.000092

(0.000032) -0.000061

(0.000031) *- 0.000033

(0.000044) -0.000084

(0.000047) -0.000047

(0.000029) — 0.000038

(0.000028) *- 0.000010

(0.000042) -0.000054

(0.000039)

0.0885 +6.20

(2.16) +6.89

(3.12) +5.45

(3.19)

— 0.262

(0.088) -0.246

(0.122) -0.237

(0.138)

+0.088

(0.055) +0.201

(0.077)

* +0.008

(0.085)

+ 7.55

(3.55) + 10.37

(4.17) + 7.28

(5.94)

+0.315

(0.214) +0.492

(0.273) *+0.063

(0.384)

+0.260

(0.208) +0.486

(0.308) *+0. 162

(0.327)

0.0827

0 . 0798

0.0878

0.0914

+ 6.44

(2.14) +7.83

(3.02) +5.87

(3.16)

— 0.290

(0.079) -0.301

(0.117) -0.255

(0.112)

+0.075

(0.055) +0.175

(0.075) *-0.011

(0.083)

+6.76

(3.52) +9.07

(4.64) +6.30

(5.86)

+0.305

(0.211) +0.527

(0.273) *-0.044

(0.361)

+0.295

(0.200) +0.547

(0.306) *+0.099

(0.281)

0.0829

0.0801

0.0876

-6.500

(1.183) -5.213

(1.162)

0.0869

**+0.0711

(0.0429) +0.0146(0.0055) +5.16(2.03) -0.206(0.077) **+0.090(0.052) + 7.42(3.23) 0.0792

expansion divided by the percentage shrinkage, for concretes having a nominal 5}/i bags of

ious independent variables (AREX =AEXP/ASHR)

for 8 weeks and then placed in water for 4 weeks.

NajO MgO WAGN Li SrO Mn Rb Zn Ba W/C ASHR S.D.

-0.539

(0.400) 0.0952

+0.1082 0.0874

(0.0420) +0.1023

(0.0475) +0.1519

(0.0814) +0.0732

(0.0627) +0.0934

(0.0424) +0.0924

(0.0470) +0.1347

(0.0806) +0.0616

(0.0588)

+0.0200

(0.0059) +0.0187

(0.0061) *+0.0083

(0.0103) +0.0253

(0.0083) +0.0177

(0.0060) +0.0182

(0.0061) *+0.0084

(0.0103) +0.0239

(0.0079)

-0.000093

(0.000033) -0.000068

(0.000032) -0.000110

(0.000053) *-0. 000025

(0.000041) -0.000055

(0.000030) -0.000049

(0.000029) -0.000081

(0.000050) *-0. 000019

(0.000035)

+5.18

(2.20) + 5.05

(3.21) +6.91

(3.29)

-0.233

(0.092) -0.342

(0.143) -0.145

(0.125)

+ 0.094

(0.057) +0.155

(0.079) *+0.020

(0.095)

+6.07

(3.64) +6.65

(5.38) + 8.35

(5.35)

+0.312

(0.215) *+0.075

(0.440) + 0.416

(0.242)

+0.254

(0.210) *+0.313

(0.365) +0.281

(0.278)

0.0828

0.0918

0.0757

0.0896 +6.04

(2.17) + 5.46

(3.16) + 7.12

(3.19)

-0.258

(0.084) -0.394

(0.136) -0. 131 (0.108)

+ 0.081

(0.056) +0.127

(0.077) *+0.018

(0.094)

+ 5.29

(3.60) +5.33

(5 . 30) + 7.93

(5.22)

+0.307

(0.212) *+0.105

(0.434) +0.393

(0.233)

+0.285

(0.201) +0.408

(0.360) *+0.228

(0.241)

0.0829

0.0921

0.0748

-6.328

(1.259) -5.143

(1.220)

0.0877

*+0.0778

(0.0442) +0.0158

(0.0057) +5.05

(2.06) **-0.181(0.087)

** + 0.095

(0.054) +6.85

(3.32) 0.0796
Table 10-34. Calculated contributions to the ratio, percentage expansion after 28 days in water divided by the percentage shrinkage after 56 days in laboratory air, for concretes having a nominal 53^2 of cement per cubic yard and a slump of 5 ± 1 in., and the calculated ranges of such contributions {AREX=AEXP/ASHR)

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (3) table 10-33

Calculated contri- butions to AREX

Calculat- ed ranges

of contri- butions

to AREX

Const. = +0.928

C3A**... 0 to 15 -0.0042 0 to -0.063 0.063 C2S**—

.

5 to 50 -0.00154 -0.008 to -0.077 0.069 C4AF 4 to 17 -0.0090 -0.036 to -0.1.53 0.117 Na^O 0 to 0.75 -1-0.1023 0 to +0.077 0,077 MgO 0 to 5.0 +0.0187 0 to +0.094 0.094 WAGN.. *1300 to 2900 -0.000068 -0.088 to -0.197 0.109 Li 0 to 0.02 -1-5.18 0 to +0.104 0.104 SrO 0 to 0.4 -0.233 0 to -0.093 0.093 Mn 0 to 1.0 +0.094 0 to +0.094 0.094 Rb** 0 to 0.01 + 6.07 0 to +0.061 0.061 Zn** 0 to 0.2 +0.312 0 to +0.062 0.062 Ba** 0 to 0.2 +0.254 0 to +0.051 0.051

*cmVg.

•Coefficient of doubtful significance as coef./s.d. ratio was less than 2.

A corresponding series of calculations for the

Series A concretes made of NAE cements is presented in table 10-39. Increases in SrO, and

possibly FeaOs and fineness were associated

with an increase in the ratio. Increases in NaoO

and Li may possibly be associated with de- creases in the ratio.

6.7. Shrinkage of Tops and Bottoms of Concrete Specimens as Cast

All of the data presented in this section on

shrinkages and expansions, their differences,

and their ratios have been based on averages

of the measurements of the tops and bottoms

of the specimens as cast. The results of meas- urements on the top of the concrete specimens

and the bottom as cast usually differed. The

frequency distribution of these differences obtained on the concretes of constant water/cer

Table 10-3.'> Frequency distribution of cements with respect to the ratio (OSHR-OEXP)/OSHR of concretes having a nominal 5}4

bags of cement per cubic yard and a water-cement ratio of 0.635

Ratio

-0.10 -0.05 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Type cement to to to to to to to to to to to to to and Total -0.05 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 over

Number of cements

I 1 0 1 1 1 6 14

2

3

14

1 11

19 153

14

16

15

5

29

2 3 82

868

220

3

15

lA

II 1 2 4 5 18

14

13

1 IIA

III 2 3 4 1 IIIA 1 IV, V 1 2 2 2 Total 1 0 2 3 6 14 24 32 46 45 19 2 1 3 198

64
Table 10-36. Frequency distribution of cements with respect to the ratio {ASHR-AEXP)fASHR of concretes having a nominal 5]^

bags of cement per cubic yard and a slump of 5 ± 1 in.

Type cement

Ratio

Total

0

to 0.05

0.05

to 0.10

0.10

to 0.15

0.15

to 0.20

0.20

to 0.25

0.25

to 0.30

0.30

to 0.35

0.35

to 0.40

0.40

to 0.45

0.45

to 0.50

0.50

to 0.55

0.55

to 0.60

Number of cements

I 1 3 4 8 7

17

13

19

1 12

12

13

16

1 20

10

2

9

5

15

2

22

3 78

8

66

2 20

3

15

lA

II 5 2 4 IIA

III 1 10

15

3

14

1 IIIA

IV, V 1 2

Total 1 8 8 12 21 39 53 29 12 6 0 3 192

I

I ment ratio are presented in table 10-40. Although there were 12 instances where the

i bottom of the specimen had greater shrinkage

! than the top, the tops of the majority of the

1 specimens had greater shrinkage than the bot-

: toms. The equations presented in table 10-41

indicate that this difference was associated

with higher average shrinkage (OSHR), as inI dicated in eqs 1 and 5 (see also table 10-44).

j The reduction in variance resulting from the

I use of the additional independent variables in

eqs 4 or 8 was significant at the 5-percent

: probability levels. The use of only commonly

determined variables in eq 2, or those with

trace elements in eq 3, resulted in a reduction

in the S.D. value significant at the 5-percent

probability level. In eqs 6 and 7, the reduction

in the S.D. was not significant at the 5-percent

; level (see table 10-44). Of the different independent variables in tables 10-41, only OSHR,

the average shrinkage of the top and bottom

as cast, had a coef./s.d. ratio greater than 3. The frequency distribution of the differences

of the shrinkage of tops and bottoms of the

specimens as cast of the Series A concrete specimens is presented in table 10-42.

Equations are presented in table 10-43 indicating the relationship of the various independent variables to the difference in the shrinkage of the tops and bottoms of the Series A

concrete specimens. The use of commonly determined variables in eqs 1, 3, 5, and 7 resulted

in a significant reduction in the S.D. values (see

also table 10-44). The additional use of the

trace elements, Cr, Kb, Li, and Ni in eqs 2, 4,

6, and 8 respectively, each resulted in a reduction in variance significant at the 1-percent

probability level (see table 10-44).

A similar series of equations (not presented

in tables) was calculated using the percentage

65
Table 10-37. Coefficients for equations relating the {shrinkage-expansion) /shrinkage ratios ables; the 6- x 8- by 16-in. concrete specimens were cured in moist air for 14 days, then

Equation

Type

cement Note Const. NaaO MgO

AE+NAE (') _l_n QQQQ -0.1664 *-0.0083

S.d. = (0.0610) (0.0491) (0.0060) NAE (2) OEXR = 4-0.3584 -0.1757 *- 0.0088

B.d. = (0.0654) (0.0518) (0.0063) AE+ NAE (») AEXR = +0.1939 -0.0808 -0.0157

s.d. = (0.0630) (0.0455) (0.0057) NAE {') AEXR = +0.1723 -0.0939 *-0.0181

s.d. = (0.0652) (0.0465) (0.0059)

» 178 cements; Avg = 0.3091; S.D. = 0.1037.

2 166 cements; Avg = 0.3063; S.D. = 0.1054.

» 172 cements; Avg = 0.2957; S.D. = 0.0937.

« 160 cements; Avg = 0.2926; S.D. = 0.0937.

Coef./s.d. ratio was less than 1 in equations for "odds" and "evens".

Table 10-38. Calculated contributions to the OEXR ratio or (OSHR-OEXP)/OSHR, of concretes of nominal bags of cement per cubic yard and a water-cement ratio of 0.635, and

the calculated ranges of such contributions

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (2) table 10-37

Calculated contri- butions to OEXR

Calculat- ed ranges

of contri- butions

to OEXR

Const. = +0.3584 Na:0 0 to 0.75 -0.1757 0 to -0.1.32 0.132 MgO**... 0 to 5.0 -0.0088 0 to -0.044 0.044 SOi 1.2 to 3.0 -0.0523 -0.063 to -0.157 0.094 WAGN** *1300 to 2900 +0.000049 +0.064 to +0.142 0.078

Li 0 to 0.02 -5.042 0 to -0.101 0.101 Rb 0 to 0.01 -8.542 0 to -0.085 0.085 SrO 0 to 0.4 +0.4648 0 to +0.186 0.186 Ba** 0 to 0.2 -0.2521 0 to -0.0.50 0.050 V** 0 to 0.1 -0.7135 0 to -0.071 0.071 p** 0 to 0.5 -0.1011 0 to -0.050 0.050 Pb 0 to 0.05 +2.741 0 to +0.137 0.137

Table 10-39. Calcidated contributions to the AEXR ratio or {ASHR-AEXP)/ASHR of concretes of nominal 5]/2 bags of cement per cubic yard and a slump of o ± 1 in., and the calculated ranges of such contributions

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq (4) table 10-37

Calculated contri- butions to AEXR

Calculat- ed ranges

of contri- butions

to AEXR

Const. = +0.1 723 Na20 0 to 0.75 -0.0939 0 to -0.070 0.070 MgO 0 to 5.0 -0.0181 0 to -0.090 0.090 Fe20' 1.0 to 5.0 +0.0184 +0.018 to +0.092 0.074 WAGN.- *1300 to 2900 + 0.000056 +0.073 to +0.162 0.089 Li 0 to 0.02 -5.462 0 to -0.109 0.109 Rb** 0 to 0.01 -3.889 0 to -0.039 0.039 SrO 0 to 0.4 +0.2834 0 to +0.113 0.113 Ba** 0 to 0.2 -0.2355 0 to -0.047 0.047

*cmVg.

**Coefficient of doubtful significance as coef./e.d. ratio was less than 2. cmVg.

Coefficient of doubtful significance as coef./s.d, ratio was less than 2.

Table 10-40. Frequency distribution of cements with respect to the difference of the percentage shrinkage of the top and bottom of speci- mens as cast of concretes having a nominal 5]/2 bags of cement per cubic yard and a water-cement ratio of 0.636 (ODSH)

Type cement

Difference in percentage shrinkage of top and bottom

Total -0.006to -0.004

-0.004

to -0.002

-0.002

to 0.000

0.000

to 0.002

0.002

to 0.004

0.004

to 0.006

0.006

to 0.008

0.008

to 0.010

0.010

to 0.012

0.012

to 0.014

0.014

to 0.016

0.016

to 0.018

Number of cements

I 3 3 5

1 11

16 21

220

20

4

7

14

10

15

2 1 1 82

867

1 19

3

14

lA

II 1 1 2 15 2 2 1 IIA

III.. 4 3

14

6

2

1

2 IIIA

IV, V 1 1 1 2 1 2 1 Total 2 4 6 22 39 52 38 19 6 3 2 1 194

66
of the concretes of nominal 5]/2 bags of cement per cubic yard to other independent vari- dried in laboratory air for 56 days, then placed in water for 28 days

SOa

Air

content FeaOs WAGN Li Rb SrO Ba V P Pb S.D.

— 0.0515

(0!0204 — 0 0523

(0;0215)

* — 0.0124

(0.0100)

* +0.000049

(0.000029) *+ 0.000049

(0.000031) + 0.000045

(0.000027)

* +0.000056

(0.000028)

-5.750

(2.432) *-5.042

(2.520) -5.857

(2.112) -5.462

(2.148)

-9.889

(3.621) -8.542

(3.804) -5.434

(3.408) *-3.889

(3.480)

+0.4.542 (0.0867) +0.4648

(0.0933) +0.3182

(0.0778) +0.2834

(0.0827)

*-0.2838

(0.2261) *-0.2521

(0.2329) *-0.2530

(0.1968) *-0.2355

(0.1984)

*-0.7141

(0.4479) *-0. 71.35 (0.4614)

*-0. 1190

(0.0638) *-0.1011

(0.0663)

*+2.698

(1.142) *+2.741

(1.163)

0.0874

*+0.0156

(0.0088) +0.0184

(0.0088)

0.0880

0.0829

0.0829

shrinkage (ASHR) as an additional indepen- than 3 was obtained for ASHR in an equation

dent variable. A coef./s.d. ratio slightly greater relating ADSH to ASHR.

7. Discussion

7.1. Comparison of Equations for the Dependent Variables

A summary of equations for shrinkage and

expansion characteristics of the Series O concretes using AE + NAE cements is presented

in table 10-45. The equations are presented

vertically instead of horizontally as was also

done in previous Sections. Also presented are

the coef./s.d. ratios of each of the independent

variables as well as the calculated ranges of the

effects of these independent variables. It may

be noted that in the first two equations (OSHR

and OEXP) , columns 1 and 2, increases in SO3

and loss on ignition were associated with de- creases in both shrinkage and expansion. In- creased Na20 was associated with decreased

shrinkage. Both the shrinkage and the expansion increased with increased C3A, C4AF, fine- ness of the cement and the air content of the

concrete.

It was previously indicated (tables 10-1 and

10-2) that concretes made with the air-entraining cements had lower cement content per unit

volume than the others. There was, however,

also probably a decrease in water content, and

in fine and coarse aggregate per unit volume of

concrete with an increase in air content. A de- crease in the cement content may be expected

to result in a decrease in the shrinkage [1].

L'Hermite [1] quoting Dutron [6] indicated

that the shrinkage of concrete,

^6 = 7 (e + c-fv-|-/)» where e volume of water, c = volume of cement, v =

volume of voids, and / = volume of fines. It was not possible in our present series of tests to hold the cement content constant and vary

only the air content. The void volume or air

content appears to have a major effect when

airentraining cements are included. Tables

10-5 and 10-9 indicated that for NAE ce- ments, the air content had a coef./s.d. ratio

less than 1 and was not a significant variable.

The slump of the concretes made with AE ce- ments was previously reported [3] as being

high when a constant water/cement ratio was

used. When the water content was adjusted to that required to produce the 5 ± 1-in-slump

concretes, the air content still appeared to be

associateci with shrinkage, but not with ex- pansion (see table 10-46).

The equations for the differences between the

shrinkage on drying and the expansion on re- wetting (i.e., the residual shrinkage) are presented in columns 3 and 4 of table 10-45. Column 3 indicates that increases in C4AF, C3A/

SO3, fineness, and SrO were associated with

increases in the residual-shrinkage values. In- creases in Loss, Rb, and possibly Na20, and Li were associated with decreases in these values

in column 3 where the percentage shrinkage was not used as an independent variable. The

greater the initial shrinkage, the greater the

residual shrinkage, as indicated in column 4. Except for Rb and SrO, none of the other independent variables had coef./s.d. ratios

greater than 2 for the equation presented in

column 4.

67
OlOO

CD Tj< oo

oo88

do

«D10 OO

oooo

do

OM* dd+'-'

OlO ooo Ofo rot^ -to rtO oo oo00 t-*

•-HO dd

o oo

dd+-'

CO N OO

dd

oo

dd

IM r-H OO

dd

too

CiCO

(N »-* OO

dd

OO

dd

lOCO

05C0 OO

OOO oo

I ^ ooI ^

too

(MM

CO oo

tocoo

CO <M OOoo

dd+^

oco 040

COoo

dd

r^o

COM OOoo

dd

t^to Ort

cocs oo

dd ooOOO

00oooooo

dd

I

00 IN t^OO OOoooo

dd

I

OS toO to »o oooo

— 00

to o tooo

OO

t~ CO -Jl (N

irjio lOlO

CO '-' CO — oo oo OO

lOOO

co-^ M r-l oo

OOO

CO i-H CO ^ oo oo

oo oo oo

I ^ ooI ^

oo oo oooo oo

oo+-' oo

CO-* oo

oodd+^

oooooooo

dd

too -^t^

lO OS iO C7S -HO (NO oo oo oo oo

dd dd

NO 1-1 to

to OS «o -. oo oo oooo

oo oo

NCO O -H oooo

W5tD WC^

t01> (NOO

CO <-! M rH oo oooo

00OMooCO to oooocooo too

cooo -^os

CO t-l C<l t-H oo oo

003

coco

(N(N oo

oo

u u w

oo+^

II a Km

oo

II II wm

9-a' O OQ

oo

II II oo+^

u u

9"^ O CO

oo

wO oi

oo

II II wO m

II II w

039-°:
Table 10-42. Frequency distribution of cements with respect to the difference of the percentage shrinkage of the top and bottom of speci- mens as cast of concretes having a nominal 5}A bags of cement per cubic yard and a slump of 5 ik 1 in. (A DSH)

Type cement

Difference in percentage shrinkage of top and bottom

Total -0.006

to -0.004

-0.004

to -0.002

-0.002

to 0.000

0.000

to 0.002

0.002

to 0.004

0.004

to 0.006

0.006

to 0.008

0.008

to 0.010

0.010

to 0.012

0.012

to 0.014

0.014

to 0.016

Number of cements

I 2 1 2 7

17

114

11

20

1 16

13

14

18 12

26

1 3 77

QO

65

220

314

T A II 3 1 7 11

1 2 1 IIA

III 1 112

4 8 1

11

2 IIIA

IV, V 3 2 2

Total - - 6 2 13 22 36 46 32 23 5 3 1 189

The equation for the ratio of the expansion

divided by the shrinkage (OREX) (column 5)

also indicates that the greater the shrinkage the

smaller the expansion/shrinkage ratio. In- creases in Rb and possibly NaaO, Li, and C3A

were associated with an increase in the ratio,

and increases in SrO with decreases in the ex- pansion/shrinkage ratios. Other independent

variables had coefficients of doubtful signifi- cance as related to this ratio.

The equation in column 6 for the ratio of

the difference between shrinkage and expansion divided by the shrinkage (OEXR) has

only two independent variables, Na20 and SrO,

with coef./s.d. ratios greater than 3. Increases

in SrO and possibly Pb were associated with

increases of the ratio. Increases in Na20 and

possibly Li, Rb, and SO3 were associated with

decreases of the ratio values.

A series of equations similar to those in table

10-45 is presented in table 10-46 for the Series

A concretes made of AE + NAE cements. In

general, but with a few exceptions, the same

independent variables had coef./s.d. ratios

greater than one in equations in this table and

in the previous table. The effect of the air content was previously noted and discussed.

7.2. The Effect of Trace Elements

Tables 10-45 and 10-46 show, as indicated in

previous subsections where the equations were

discussed, that the coef./s.d. ratios of the trace

elements were generally less than 3. This effect

may have resulted from the fact that the concretes contained a lower percentage of the ce- ments than did the mortars and neat pastes,

and the influence of the trace elements is thereby more difficult to determine. It may also

be that variations resulting from the use of different lots of sand and gravel in this study may

have helped mask the effects of the independent variables used in the equations. Generally,

the use of trace elements as independent variables in addition to commonly determined independent variables in the multivariable equations resulted in a reduction in variance

significant at the a = 0.01 level although there were many instances where the reduction in

variance was significant at the a = 0.05 level.

7.3. Agreement of Duplicate Determinations

of Percentage Shrinkage and Percentage

Expansion

There were 26 pairs of duplicate specimens

where the water/cement ratio was the same

for the Series 0 and Series A concretes. The

estimated standard deviation of individual

measurements from tho differences between

these pairs was 0.0016 for the shrinkage val- ues and 0.0015 for the expansion values.

A summary of the averages of shrinkage and

expansion values obtained with the NAE ce- ments is presented in table 10-47. Also presented are the S.D. values for the individual

cements and the equations, and those calculated from duplicate determinations. The

(S.D.)' values for all the cements were from

5 to 12 times the (S.D.)^ values obtained from

the duplicates.

It has been indicated in previous tables that,

by use of various independent variables, a

highly significant reduction in variance was

obtained. The S.D. values of the "best" equations were, however, much greater than the

S.D. values of the duplicate specimens. Each of

these pairs of duplicate specimens was made

the same day using a single lot of aggregates.

Greater variations could be expected if the test specimens were made over a period of three

years with different lots of aggregates and by

different operators. This necessary procedure

may also have affected the shrinkage and ex- pansion values as measured and may have

masked to some extent the effect of the independent variables, such as cement composition, on these properties. No control tests were carried on during the period the specimens of the

69
OlOO do

COCO do

(NO

00 00 -HO

•ooo

>ooo rtO do

4SI

O-H

-lO doI ^

05•-HO -IO

lOO

oco

CIOO

ddI

00OO

ddI ^

CO 00

1-1 c»

»-« ddI ^

'DID OOI ~-'

COCO

lOCO

Or-1

OS CO

todd

coo

coco rHO dd

coco OSIM OO

ddI

05<0 OO

dd

00 lO«o OO

ddI ^

(N 00

C^rtO OO

to to

CO ^ C^ "O -HO OO OO

OO OO oto^ o OOOO

ddI ^

lOOS oto

CO TJH t31 -HO -HO OO OO OO OO

OO OO

OOO (M»0

CO -i^ -HO -HO OO OO OO

OO OO

CO to O-HO OOOO

dd

IN CO

CO <>i -HO OO

t^to toco O C4 CO «0 -HO OO OO

dd dd

o>co OOO

coo OO

dd

ICI -H 00 00 coo OOOO

dd+^

<N 00 coo OO

dd+^

tOrJi Ci 00 coo OO

OO

dd I -M -H OO

ddI ^

rH -H IN CO -H -H OO OO OO OO OO

OO OO

OOOO

O CO C3i OCO I^C^l -HO OO OO OO OO

OO OO

OO tOOi O CO to OJ -HO OO OOOO

OO OOI ^ OOI ^

lO OS COO OO

dd+"

II II

010 oto iOO t^TjH -H O -H OO OO OO

dd dd

11 II II II a-6

I> to O-H OO

do+"

II II K

COP-d"

<! 10

-H t^O OJO * -H ll< -H OO OO

OO

CO Til CO

O t>- O CO -H-H O-H OO OOOO

OO

II II IIy

WK

CO CO

<J ai < to"

OO+~-'

II II Km

OO

p. 0^

70
Table 10-44. "F" Values for significance of reduction of vari- ance due to added variables Table 10-44. "F" values for significance of reduction of vari- ance due to added variables—Continued

Table Equations

ratio D.F.

Critical "F" Ratio

a = 0.01 a = 0.05

10-4 *0,

1

6. 20 2:175 4.72 3.05

0,2 20.97 9:168 2.51 1.93 2,3 3.92 3:165 3.88 2.67 0,4 23.19 8:169 2.61 2.00

4,5 3.71 3:166 3.88 2.67

10-5 --- **0,

1

5.07 2:163 4.73 3.05 0,2 20.87 8:157 2.62 2.00

2,3 3.76 3:154 3.90 2.67 0,4 23.44 7:158 2.75 2.07 4,5 3.51 3:155 3.90 2.67

10-8 *0,2 4.69 2:169 4 72 3.05

0,3 18. 07 9:162 2^52 1^93 3,4 3.65 3:159 3.89 2.67

0,5 19.93 8:163 2.62 2.00

5,6 3.68 3:160 3.89 2.67

10-9 **0,

1

2.72 2:157 4.74 3.05

0,2 7. 14 2:157 4^74 3!05 0,3 19.04 8:151 2.63 2.00

3,4 3.41 3:148 3.90 2.68

0,5 21.28 7:152 2.76 2.07 5,6 3.66 3:149 3.90 2.68

10-12- *0,

1

3.20 2:174 4.72 3.05

0,2 16.67 7:169 2.74 2.07 2,3 3.77 5:164 3.13 2.27 0,4 17.89 7:169 2.74 2.07

4,5 3.62 5:164 3.13 2.27

10-13 **0,

1

1 .51 2:162 4 73 3 05 0,2 15. 16 6:158 2

'.93 2.15 2,3 4.73 5:153 3.14 2.27 0,4 16.65 6:158 2.93 2.15

4,5 4.48 5:153 3.14 2.27

*0,2 3,56 2:169 4.72 3.05 0,3 6. 17 4:167 3 42 2 . 43 3,4 13.20 6:161 2^93 2!l5 4,5 3.66 4:157 3.43 2.43

0,6 12.90 9:162 2.52 1.93 6,7 3.52 4:158 3.43 2.43

10-17 **0,2 3.60 2:157 4.74 3.05

0,3 6. 10 4:165 3.43 2.43

3,4 15.23 5:150 3.14 2.27

4,5 4.13 4:146 3.45 2.44 0,6 14.27 8:151 2 63 2 00

6,7 4.00 4:147 3^44 2!44

10-20 *0,1 7.74 7:170 2.74 2.07

1,2 10.36 3:167 3.88 2.67 0,3 117.05 2:175 4.72 3.05

3,4 6. 11 6:169 ^ . 10

10-21 **0,

1

7.87 7:158 2.75 2.07

1,2 7.40 3:155 3.89 2.67

0,3 67.95 3:162 3.89 2.67 3,4 5.00 7:155 Z . < 0 / . U/ 10-24 . . *0,

1

7.01 7:164 2.75 2.07

1,2 6.50 4:160 3.43 2.43 0,3 95.03 2:169 o . uo

3 ,

4

4.56 3:166 3.88 2.67

4,5 4.79 4:162 3.43 2.43

10-25 **0,1 7.24 7:152 2.76 2.07

1,2 4.15 4:148 3 44 2 44 0,3 82.76 2:157 4.74 3.05

3,4 4. 15 4:153 3.44 2.44

10-28 *0,1 27.84 2:174 4.71 3.05 0,2 7.77 8:168 2.61 2.00

1,3 5.58 7:167 2.74 2.07

10-29 . _ . - _ **0,

1

25. 76 2:162 4.73 3.05 0,2 7.07 8:156 2.62 2.00

1,3 5.31 7:155 2.75 2.07

1,4 5.89 7:155 2.75 2.07

10-32 *0,

2

4. 17 7:163 2.75 2.07

2,3 4.94 6:157 2.93 2. 15 0,4 3.04 5:165 3.13 2.07 4,5 6.93 6:159 2.93 2.15

0 6 15 67 2:168 4.73 3.05

6[7 5!89 7:161 2.75 2.07

1 10-33 **0,2 4.65 7:151 2.76 2.07

2,3 3.87 6:145 2.93 2.15 0,4 4.33 5:153 3.14 2.27

4,5 5.29 6:147 2.93 2.15 0,6 13.14 2:156 4.74 3.05

6,7 5.77 7:149 2.76 2.07

Critical "F" Ratio Table Equations D.F.

ratio a = 0.01 a = 0.05

10-37 *0 ,

1

D . 5o 1 Q . 1 ft 2.31 1.80

0 ,

2

7 . 01 12 : 1.54 2.32 1.82

0 ,

3

D . OU Q.I ftQ 2.52 1 .93 0,4 5 . 93 9:151 2

'.53 1.93

10-41 *0,

1

5.76 2:173 4.72 3.05

0 ,

2

Z . OZ 5*170 3.12 2.27

2 ,

3

Z . OD 3.42 2.43

1 ,

4

Z

.

6' 167 2.92 2.15 A ^ 0 .\Ji z .ID.; 4.73 3.05 u , 0 Z . U1 5 ' 1 .59 3.13 2.27

6 ,

7

Z , rt'r o: iOD 3.90 2.67

0 , o

O A7 0:10/ 3. 13 2 . 27

10-43 **0,

1

5.59 4:165 3.43 2.43

1,2 9.26 4:161 3.43 2.43

0,3 6.13 4:165 3.43 2.43

3,4 9.83 4:161 3.43 2.43

0,5 7.70 4:153 3.44 2.44

5,6 7.05 4:149 3.44 2.44 0,7 8.14 4:153 3.44 2.44

7,9 7.63 4:149 3.44 2.44

*Eouation 0 refers to the variance for the values themselves with no

fitted equation for AE+ NAE cements (See footnote of Table). **As above, for NAE cements.

different concretes were made, so information on the possible effects of different lots of sand

or of manipulative differences are not available.

7.4. Shrinkage and Expansion of Concrete

versus Shrinkage Characteristics of Neat

Cement

Equations were computed to find the relationship of each of the dependent variables for concrete of this section, i.e., OSHR, ASHR, OEXP,

AEXP, ODSX, ADSX, OREX, AREX, OEXR,

and AEXR, to the dependent variables for neat

cement of the previous section, SH24, SHOT,

SH28, SH6M, SHBR, TOBR, SB/S7, and SB/

S28. The reduction in variance or "F" values were also calculated for each of the equations.

There was an indication of a relationship between OEXP and AEXP values for the concretes and SH28 and SH6M values for the neat

cements significant at the 5-percent probability

level. Neither the shrinkage values of the two

series of concretes, the differences between the

shrinkage and expansion, nor any of the vari- ous ratios showed an indication significant at

the 5-percent level of a relationship with any

of the shrinkage values obtained for the neat

cements. This lack of relationship applied to both the nonrestrained shrinkage of the neat

cements and the time of cracking of the annular rings.

There were, possibly, many factors which

contributed to this lack of correlation. The neat

cement pastes were made with a low water/

cement ratio ; the concretes with a high water/

cement ratio. The neat cement pastes hydrated

for only 24 hr prior to drying; the concretes

for 14 days. The specimens of neat cement had

71
Table 10-45. Coefficients, coef./s.d. ratios and calculated ranges of contributions of independent variables associated with shrinkage

and expansion characteristics of concretes made with a water/cement ratio of 0.635

Column 1 2 3 4 5 6

Equation 3 3 2 4 4 1

Table 10-4 10-12 10-20 10-20 10-28 10-37

Dependent variable OSHR OEXP ODSX ODSX OREX OEXR

_

+0.0139 +0.0107 — 0.00416 — 0.00466 +0.8390 +0.3398

CsA, Coef + 0.00123

8.8 0.0185 **- 0.0000835

1.6 0.004 +0.000898

5.3 0.0117 — 0.00822

4.2

0 . 0062 — 0 . 00894

o'oi61

+ 0.000595

6.0 0.0089

+0.00498

2.Q

0.0075

Coef /s d

CaS coef Coef /s d

Oalculsited range C<AF coef +0.000390

3.4

0.0051

+0.000502

3.6 0.0065 -0.00485

2.7 0.0036

Coef /s d

CSrlcul&ted ra-ii^e Na20 coef **- 0.00231

1.7 0.0017

+0. 1273 2.8

0

'. 0954

— 0. 1664 3.4

0. 1248 -0.0515

2.5 0.0927

Coef /s d

Calculated range SO 3 coef — 0.00411

5.4 0 . 0074 Coef /s d

Calculat'ed range CsA/SOt coef +0.00097

4.6 0.0094

**_ 0.000164

1 .2 0.0016 **_ 0.000231

1.4 0.0012

Coef /s d

Calculated range

]VIgO coef **4-o 0087

1

1.6 0 . 0435

**_0 0083

1 3 0.0415

Coef /s d

Calculated range

Loss coef — 0 . 00363

5.6 0.0109 +0.00000613

7.9 0.0180

— 0 . 0022

b.O o!o066 +0.0000030 6.0

0.0090

— 0.00164

3] 1 0

'. 0049 +0.00000178

3.1 0.0053

Coef /s d

Calculated range APF coef Coef /s d

Calculated range ^Vagn coef ** +0.000049

1.7 0.0784 **- 0.0124

1.2 0.1240 **-0.2838

1.3 0.0568 -5.750

2.4 0.1150 **-0.1190

1.9 0.0595 +2.698

2.4 0.1350 -9.889

2.7 0.0989

_j_Q 4542

0 . ^

T-P U . / 111

1 .

6

0. 0714

Coef /s d

Calp.llln.t.pH rfl.ngp

i^ir content coef +0.00100

5.6 0.0100

+0.000646

5.5

0 0065

+0.000296

2.0

0.0030

**- 0.000158

1.4 0.0016

Coef /s d

Calculated range Ba coef -J- \J _ ^ f QiJ

1 4 U . UOOo

2 0

0 . 087

1

Coef /a d

Calculated range — 0 . 1923 2.2

0V . 003S woo

— \i . uyoo

1 .

4

0. 0019 Coef /s d

Calculated range P coef **+0. 00369

1.9 0.0018 **-0.0518

1.5 0.0026 +0.3234

2^8

0 . 0032 **- 0.00378

1.4 0.0015

Coef /s d

Calculated range Pb coef Coef /s d

Calculated range Rb coef Q ^ 4920

3.6

0 0049 +0.0114

3.6

0 0046

— u. 00/

3 .

8

3 4 u . UUOO

_1_ -(-11. 1 1 OQisy 3 4 0 1129

\J . okjKjO 0 . 0

Coef./s.d Calculated range

SrO, coef +0.00854

2.1 0.0034 Coef /s d

Calculated range

V, coef Coef /s d

Calculated range

Zn, coef -0.0198

2.0

0 . 0040 **+0.0126

1.6 0.0063

**-0.0102

1.6 0.0020

Coef./s.d Calculated range. -

Zr, coef Coef./s.d Calculated range

See footnotes at end of table.

72
Table 10-46. Coefficients, coef./s.d. ratios and calculated ranges of contributions of independent variables associated with shrinkage

and expansion characteristics of concretes made with a water/cement ratio of 0.635—Continued

Column 1 2 3 4 5 6

Equation 3 3 2 4 4 1

Table 10-4 10-12 10-20 10-20 10-28 10-37

Dependent variable OSHR OEXP ODSX ODSX OREX OEXR

= = = —

Constant +0.0139 +0.0107 -0.00416 -0.00466 -0.8390 +0.3398

OSHR, coef... +0.5223

13.5 -7.294

Coef./s.d 6.0

Calculated range 0.0157 0.2188

* The calculated range was computed from the range of values for the cements times the coefficient for each independent variable. ** The independent variable is probably not significant as the coef./s.d. ratio is less than 2.

Table 10-46. Coefficients, coef./s.d. ratios, and calculated ranges of contributions of independent variables associated with shrinkage

and expansion characteristics of concretes having a slump of 5 ± 1 in.

Column 1 2 3 4 5 6

xjQuation 4 5 2 5

"7 o

X aDie 1 U — o lU — 1 U 10-24 - lU — 24 10—044 lu-o7

Dependent Variable Aoxlrt AEXP ADSX ADSX AREX AEXR

t_x)nstant +0.0129 +0.0085 -0.00519 +0 861

r- A t +0.001221

8.4 0.0183 — u . uuuuyuo

1 7 0.0004 +0.000918

5.3 0.0119

+0.000725

6.6 0.0108

1 .

1

0.0002 +0.000344

2.6 0.0045

Cnpf /a H Calculated range *

Coef./s.d Calculated range C4AF, coef... +0.000552

4.1 0.0072 +0.000175

2.0 0.0023

**- 0.00467

1.7 0.0607

Coef./s.d Calculated range **+0.0156

1.8 0.0702 **- 0.0808

1.8 0.0606

Coef./s.d .. Calculated range Na20, coef -0.00714

3.6 0.0054

+0.00402

2 .

3

o!oo3o

+0.0711

1.7 0.0533

Coef./s.d Calculated range KjO, coef +0.0026

2.0 0.0029 -0.00548

6.1 0.0099

Coef/s.d Calculated range

SOj, coef . -0.00784

6.7 0.0141

**+ 0.00080

1.4 0.0014

Coef./s.d Calculated range CaA/SOs, coef +0.00080

4.0 0.0078

Coef./s.d

MgO, coef **+ 0.000428

1.9 0.0021 -0.0025

5.1 0.0075 +0.00000431

7.0 0.0129

-0.000370

2.2 o!ooi8

-0.0146

2.7 0.0730

-0.0157

2 8

0'.078o Coef./s.d Calculated range

Loss, coef -0.00381

5.7 0.0114 +0.00000609

7.7 0.0183

-0.00165

3 .

2

o!oo5o +0.00000165

2 9 0!0049

Coef./s.d Calculated range. APF, coef Coef./s.d Calculated range **+0. 000045

1.7 0.0720

Coef./s.d

See footnotes at end of table.

73
Table 10-46. Coefficients, coej. s.d. ratios, and calculated ranges of contributions of independent variables associated with shrinkage

and expansion characteristics of concretes having a slump of 5 ± 1 in.—Continued

Column 1 2 3 4 5 6

Equation i 5 2 5 7 3

Table 10-8 10-16 10-24 10-24 10-32 10-37

Dependent Variable ASHR AEXP ADSX ADSX AREX AEXR

= = -

Constant +0.0129 +0.0085 -0.00519 -0.00729 +0.861 +0.1939

Air content, coef + 0.000620

4.1 0.0062

**+0. 000208

1.8 0.0021

+0.000272

2.2 0!0027Coef./s.d Calculated range

Ba, coef **- 0.2530

1.3 0.0506 -5.857

2.8

0.1171

Coef./s.d Calculated range

Li, coef _ -0.1714

2.1 0.0034 **- 0.00274

1.3 0.0027

-0.1459

2.5 0.0029 **- 0.00305

1.9 0.0030

+5.16

2.5 0.1032 **+0.090

1.7 0.0900

Coef./s.d Calculated range- Mn, coef +0.00418

2.1 0.0042 **+0.1149

1.3 0.0023 **+0. 00284

1.3 0.0014

Coef./s.d Calculated range

Ni, coef Coef./s.d Calculated range.

P, coef Coef./s.d Calculated range Rb, coef -0.2812

2.1 0.0028 +0.0108

3.5 0.0043

-0.2592

2.6 0.0026 +0.0047 2.0

0.0019

+7.42

2.3 0.0742 -0.206

2.7 0.0824

**-5.434

1.6 0.0543 +0.3182

4.1 0.1273

Coef./s.d

SrO, coef +0.00828

2.0

0.0033

Coef./s.d Calculated range- -

V, coef **+0.0237

1.5 0.0024Coef./s.d Calculated range -

Zn, coef -0.0216

2.1 0.0043 **+0. 00927

1 1 0!0046

Coef./s.d Calculated range

Zr, coef -

Calculated range -_ - ASHR, coef +0.4705

12.9 0.0141

-5.213

4.5 0.1564

Coef./s.d Calculated range _

* The calculated range was computed from the range of values for the cements times the coefficient for each independent variable. ** The independent variable is probably not significant as the coef./s.d. ratio is less than 2.

Table 10-47. Summary of averages and estimated standard

deviations of concretes made of non-air-entraining cements

Averages, cements

percent

S.D. cements

s.p.

equations S.D.duplicates

OSHR 0.0298 0.00.56 0.0039 0.0016 ASHR 0.0296 0.0056 0.0039 0.0016 OEXP 0.0203 0.0035 0.0027 0.0015 AEXP 0.0208 0.0038 0.0029 0.0015

a 1-in-square cross-section ; the concretes an approximate 6 X 8-in cross-section.

A comparison of table 9-35 of the previous

section, indicating variables associated with

shrinkage of neat cement, with tables 10-45

and 10-46 of this section, indicating summaries

of the variables associated with the shrinkage

and expansion of concretes, shows a, number of

differences. An increase in fineness of the ce- ments was possibly associated with an increase

in shrinkage of the neat cements, but the coef./

s.d. for fineness was highly significant with the

concretes. An increase in the C3A was associated with a decrease of shrinkage of the neat

cements and with an increase in shrinkage of

the concretes. Increased Na20, K2O and possibly Rb were associated with increased shrinkage of the neat cements at 7 days and 28 days.

For the concretes, an increase in Na20 was

associated with a decrease in shrinkage, and

K2O was apparently not associated with shrinkage.

74
7.5. Shrinkage and Expansion of Concretes

versus the Dynamic Young's Modulus of

Elasticity

Equations were calculated to determine the

relationship of the shrinkage, and expansion

values of the concretes to the dynamic Young's

modulus of elasticity of 3 X 4 X 16-in speci- mens made of the same concretes, cured, and

exposed to air, then soaked in M^ater in the same

manner as the 6 X 8 X 16-in specimens. The

results, as well as the reduction in variance or "F" values, are presented in table 10-48. The

nomenclature used, 0D14, OD42, OD70, and

OD98, refers to the dynamic Young's modulus

of elasticity in psi X 10 " at 14 days (after

moist-air curing), at 42 days (after 4 weeks

air-drying), at 70 days (after 8 weeks drying

in laboratory air), and at 98 days (after being

in water for 4 weeks) respectively. The equations presented in this table are for the concretes made with a water/cement ratio of 0.635.

With the number of degrees of freedom involved, 2 : 180, "F" values of 4.70 and 3.05

must be equaled or exceeded for an indication

of a relationship significant at the one or the

5-percent probability levels, respectively.

The equations of table 10-48 indicate that an increase in the dynamic modulus of elasticity

! was associated with a decrease in the amount

i of shrinkage, with a decrease in the subsequent

! expansion when the concretes were rewetted,

and with a decrease in the diiference between

Table 10-48. Relationship of percentage shrinkage (OSHR),

percentage expansion, OEXP, and percentage shrinkage minus

percentage expansion of concrete (ODSX) versus the dynamic

1 modulus of elasticity of concrete specimens at various ages

Equation S.D.

1 OSHR = +0.0540

(0.0054) -0.00497 CD 14 0. 00552 9. 7 s.d.= (0.00113)

2 0SHR = +0.0607

(0.0051) -0.00661 OD42 0 00531 17. 7 s.d.= (0.00111)

3 OSHR = + 0.0619

(0.0045) -0.00709 OD70 0 00514 25 0

s.d.= (0.00100)

4 OSHR =

s.d.= +0.0681(0.0070) -0.00743

(0.00137) OD98 0 00539 14 7

5 0EXP = +0.0315

(0.0037) -0.00225 0D14 0 00381 4 2 s.d.= (0.00078)

6 OEXP = + 0.0363

(0.0036) -0.00337 OD42 0 00371 9 4 8.d.= (0.00078)

7 0EXP = +0.0366

(0.0032) -0.00355 OD70 0 00365 12 4 s.d.= (0.00071)

8 0EXP = +0.0429

(0.0048) -0.00434 0D98 0 00369 10 7 s.d.= (0.00094) 9 ODSX = +0.0224

(0.0039) -0.00272 OD14 0 00403 5 4 s.d.= (0.00082)

10 0DSX =

s.d.= +0.0244

(0.0039) -0.00324(0.00083) OD42 0 00399 7 5

11 0DSX =

s.d.= +0.0393(0.0034) -0.00354

(0.00077) OD70 0 00393 10 7

12 0DSX =

s.d.= +0.0252

(0.0053) -0.00309

(0.00103) OD98 0 .00405 4 5

the percentage shrinkage and percentage ex- pansion, ODSX. The indication of relationship

in eqs 5 and 12 were significant at the 5-percent

level and in the others at the 1-percent level. In table 9-36, Section 9, a series of equations was presented for the shrinkage of neat cement

pastes versus the compressive strengths of

1 : 2.75 (cement to sand) mortars. Higher

strength of the mortars at 1, 3, and 7 days was

associated with higher shrinkage of the neat

cements at 24 hr (after 24 hr moist curing).

There was no significant relationship between

the shrinkage of the neat cements at later ages,

up to 6 months, and the compressive strength of

mortars at 1, 3, 7, or 28 days. An increase in

the compressive strength of the mortars was

associated with a decrease in the time of the

annular specimens made of neat cement of nor- mal consistency.

A series of equations was also calculated for

the concretes made with sufficient water to give

a 5 ± 1-in slump. These equations and the "F"

values, though not presented here, were very

similar to the relationships presented in table

10-48 for constant water/cement ratio concretes.

It has been reported that shrinkage increases

with an increase of the cement content of the

concrete [1]. An increase in cement content

would also result in a greater compressive

strength and a higher dynamic modulus of

elasticity. With any one cement there would

be a greater amount of cement gel formed per

unit volume in a given period of hydration if there was more cement to start with. The results of the present study indicate that greater

shrinkage occurred with lower strength (lower

dynamic E), and that concretes with higher

strengths had lower shrinkages. The compounds

and other independent variables associated with

the shrinkage of concretes have been reported

in this section; variables associated with dynamic Young's modulus of elasticity will be re- ported in a later section in this series.

7.6. Top and Bottom Shrinkage and Expansion

The greater shrinkage of the tops of a majority of the specimens as cast is probably the

result of settlement of the solids and normal

bleeding. The actual water/cement ratio in the

upper half of the 8-in depth of concrete at the

time of setting may have been greater than in

the bottom half, and such a difference could

account for the greater shrinkage. It was noted

that concretes with greater shrinkage of the

top of the specimens when air dried usually

had a greater expansion when the specimens were rewetted. Attempts were made (without

success) to relate the difference in expansion

of the tops and bottoms of specimens to various

75
independent variables. The differences were

usually slight, and the limitations of the measuring device, and the fact that in one case averages of two measurements and in the other

case single measurements were used, may have

masked any relationship.

7.7. Comparative Test Values on other Hydraulic Cements

Tests were also made of concretes made of

two portland-pozzolan cements and seven portland-blast-furnace-slag cements. All but one of

the nine cements had shrinkage values in the

"0" series within the range of values of the

concretes made of the portland cements. Concretes made of six of the nine cements had

greater shrinkage and expansion values than

the averages of the NAE portland cements. All

the concretes were proportioned on a weight

basis rather than a volume basis. The lower

specific gravity of these cements resulted in a

slightly greater volume of cementitious material in the concrete than would be the case with the Portland cements.

8. Summary and Conclusions

(1) Two series of concretes were made with

199 Portland cements having a broad range of

composition and properties. In Series 0 the

water/cement ratio was 0.635, and in Series A

the water/cement ratio was adjusted to give

concretes with a 5 ± 1-in slump. Although designed for a cement content of 5.5 bags per

cubic yard, the computed cement contents of

concretes made of the air-entraining cements were considerably less than this value.

(2) Specimens, 6 X 8 X 16 in, were made of

the two series of concretes with each of the

cements. Measurements were made of the

shrinkage of the specimens when stored in

laboratory air for 8 weeks after an initial 14-

day curing period. After the drying period, the

specimens were stored in water for 4 weeks

and measurements made of the expansion.

(3) Calculations were made of the difference

between the percentage shrinkage and the percentage expansion, of the ratio of the expansion to initial shrinkage, and of the ratio of the

difference to the initial shrinkage.

(4) The average shrinkage of the concrete

specimens was 0.030 percent, with a range of

about 0.015 to 0.045 percent. The estimated

standard deviation of individual measurements

obtained from duplicate specimens was 0.0016.

(5) The average expansion of the air-dried

concrete specimens when resoaked for 4 weeks was 0.020 percent, with a range of 0.011 to 0.035 percent. The estimated standard deviation of measurements on duplicate specimens

was 0.0015.

(6) The frequency distribution of the

shrinkage and expansion for the concretes, as

well as the residual shrinkage and ratios of

shrinkage and expansion values of the concretes, indicated, in each instance, a fairly wide

distribution of values. There was an overlapping of the shrinkage and expansion values

obtained with the different types of cement as

classified. (7) Multivariable regression equations were

used to determine which of the available independent variables or combinations of variables,

such as cement composition, trace elements,

fineness, and the air content of the concrete, were associated with the shrinkage and expansion characteristics. Typical equations are presented in table 10-45 for the concretes made

with a 0.635 water/cement ratio.

(7.1) Increases in C3A, C4AF, fineness of the

cement, and air content of the concrete were » all associated with increases in both the shrink- i age and the expansion values of the concretes. !> (7.2) Increases in Na20, SO3, and loss on 11 ignition of the cements were associated with ' decreases in the shrinkage values of the concretes. Increases in SO3 and loss on ignition were associated with decreases of the expansion values of the concretes.

(7.3) There was no highly significant indication of association of any of the individual

trace elements of the cements with either the

shrinkage or the expansion of the concrete. An

increase in Rb may possibly be associated with an increase in expansion, an increase in SrO

possibly with an increase in shrinkage, and an

increase in Zn possibly with a decrease in

shrinkage values. The trace elements of P, Pb,

and Zr may possibly have an effect, but verifi- cation of their influence would require further

investigation. The additional use of all the trace

elements having a coef./s.d. ratio greater than

1 in the equations with the commonly determined variables usually resulted in a highly

significant reduction of variance.

(7.4) The difference between the initial drying shrinkage and the subsequent expansion

when the concrete specimens were rewetted 1 (i.e. the residual shrinkage) was highly dependent on the values for the initial shrinkage.

Equations calculated with only the cement composition and the air content as independent

variables indicated that increases in C4AF,

C3A/SO3, fineness, SrO, and possibly air content of the concrete were associated with in- creases in the residual-shrinkage values. In- creases of loss on ignition, Rb, and possibly

Na20 and Li were associated with decreases in

the residual-shrinkage values. When the initial

76
shrinkage was included as an independent variable, only Rb and SrO were related to the

residual shrinkage. Sodium oxide, C3A/SO3,

MgO, air content and Li had coef./s.d. ratios

between one and two and were possibly not as- sociated with residual shrinkage, but further

study of their effects may be warranted.

(7.5) The ratio of expansion/shrinkage val- ues was highly dependent on the initial shrinkage value. Increases in Rb, and possibly Na20,

Li, and C3A were associated with higher ex- pansion/shrinkage ratios. Increases in SrO as

well as the initial shrinkage were associated

with decreases in the expansion/shrinkage

ratio.

(7.6) The equations for the ratio of residual

shrinkage divided by the shrinkage had only

two independent variables that were highly

significant. Increases in SrO and possibly Pb

were associated with increases in the ratio. In- creases in NaoO and possibly SO3, Li and Rb

were probably associated with decreases in the

ratio.

(7.7) Equations calculated for the shrinkage, expansion, differences, and expansion/

shrinkage ratios of specimens made of concretes having a 5 ± 1-in slump were in general

agreement with those calculated for the 0.635-

water/cement-ratio concretes. Some differences

may be noted in comparing tables 10-45 and

10-46.

(7.8) In equations calculated for the non-airentraining cements, the coef./s.d. ratio for aircontent of the concretes was usually less than 1 and always less than 2. (7.9) Equations calculated using the principal oxides instead of the potential compounds

resulted in approximately the same estimated

standard deviations and reduction-in-variance

values.

(8) The shrinkage values of the two series

of concrete specimens moist cured for 14 days

and then air dried did not show, at the 5-percent probability level, a relationship to the

shrinkage values of the neat cement bars of

normal consistency, moist cured for 24 hr, and

then air dried.

(9) The shrinkage and expansion values of

the two series of concrete specimens did not

show at the 5-percent level a relationship with

time of cracking of the restrained annular

specimens made of the neat cement, moist

cured for 24 hr and then air dried.

(10) _ Higher shrinkage values and higher

expansion values of the concretes were asso- ciated with lower dynamic modulus of elasticity values of the concretes.

Acknowledgments are made to R. A. Clevenger who supervised the proportioning of the

concrete, fabrication of the specimens, and

making of measurements. Acknowledgments

are also made to Elden Steward, A. C. Figlia,

and other members of the staff for their able

assistance in conducting the tests.

9. References

[1] L'Hermite, R. G. Volume changes of concrete, Proceedings of the Fourth International Symposium

on the Chemistry of Cement, 1960, Washington,

NBS Mono. 43, Vol 2, p. 659-702.

[2] Swayze, M. A. Discussion, (same as reference above) , p. 700-702.

[3] Interrelations between Cement and Concrete Products, Part 1, NBS Building Science Series No. 2, Aug. 20, 1965. Section 1, Materials and techniques, by R. L.

Blaine, H. T. Ami, and B. E. Foster. Section 2, Water requirements of portland ce- ment, by R. L. Blaine, H. T. Arni, and

R. A. Clevenger.

Section 3, Occurrence of minor and trace ele- ments in Portland cement, by R. L. Blaine, Leonard Bean, and Elizabeth K. Hubbard.

[4] Interrelations between Cement and Concrete Products, Part 2, NBS Building Science Series No. 5, July 1, 1966.

Section 4, Variables associated with expansion

in the potential sulfate expansion test, by R. L. Blaine, H. T. Arni and D. N.

Evans.

Section 5, Heat of hydration of portland cement,

by R. L. Blaine and H. T. Arni.

Section 6, Variables associated with small autoclave expansion values of portland ce- ments, by R. L. Blaine and H. T. Arni.

[5] Interrelations between Cement and Concrete Properties, Part 3, NBS Building Science Series No. 8, April 1968. Section 7, Compressive Strength of Test Mortars, by R. L. Blaine, H. T. Arni, and M. R. DeFore.

Section 8, Compressive strength of steam-cured

Portland cement mortars, by R. L. Blaine, H. T. Arni, and M. R. DeFore.

[6] R. Dutron, Le retrait des ciments et betons, Ann.

Trav. Publ. de Belgique (April-June 1934).

{(11.S. GOVERNMENT PRINTING OFFICE: 1969 0—321-131

77
RELATED PUBLICATIONS

NfeS Monograph 43—Chemistry of Cement Proceedings of the

Fourth International Symposium—Washington 1960. Presented in two volumes. Volume I—$6.50. Volume II—$6.25.

The two volumes at $12.75 a set. (Originally issued September

1962, and reprinted February 1964.)

NBS Building Science Series 2, 5, and 8—Interrelations between

Cement and Concrete Properties. Part 1—35 cents. Section 1, Materials and Techniques. Section 2, Water Requirements of

Portland Cement. Section 3, Occurrence of Minor Trace Elements in Portland Cement. Part 2—35 cents. Section 4, Variables Associated with Expansion in the Potential Sulfate Expansion Test. Section 5, Heat of Hydration of Portland Cement.

Section 6, Variables Associated with Small Autoclave Expansion Values of Portland Cements. Part 3—55 cents. Section 7, Compressive Strength of Portland Cement Test Mortars. Section 8, Compressive Strength of Steam-cured Portland Cement

Mortars.

NBS Building Science Series 17—Causes of Variations in Chemical Analyses and Physical Tests of Portland Cement. (In press.)

* Order publications from Superintendent of Documents, Government

Printing Office, Washington, D.C., 20402. (For foreign mailing, add one- fourth of the price of the publication.)
i ANNOUNCEMENT OF NEW PUBLICATIONS IN

BUILDING SCIENCE SERIES

Superintendent of Documents,

Government Printing Office,

Washington, D.C., 20402

Dear Sir:

g I Please add my name to the announcement list of new publications to be issued in the series

:

National Bureau of Standards Building Science Series.

Name

Company

Address

City State Zip Code

(Notification key N-339)


I

I

i

1

I

J
NBS TECHNICAL PUBLICATIONS

I PERIODICALS

I

I JOURNAL OF RESEARCH reports National

! Bureau of Standards research and development in

I physics, mathematics, chemistry, and engineering,

i Comprehensive scientific papers give complete details

! of the work, including laboratory data, experimental

j procedures, and theoretical and mathematical analy-

' ses. Illustrated with photographs, drawings, and

I charts.

: Published in three sections, available separately:

• Physics and Chemistry

Papers of interest primarily to scientists working in

' these fields. This section covers a broad range of

I physical and chemical research, with major emphasis

j on standards of physical measurement, fundamental

I constants, and properties of matter. Issued six times

I a year. Annual subscription: Domestic, $6.00; for-

\ eign, $7.25*.

i

I • Mathematical Sciences

I

! Studies and compilations designed mainly for the

mathematician and theoretical physicist. Topics in

i mathematical statistics, theory of experiment design,

'\ numerical analysis, theoretical physics and chemistry, logical design and programming of computers

I and computer systems. Short numerical tables. Issued quarterly. Annual subscription: Domestic,

I $2.25; foreign, $2.75*.

|« Engineering and Instrumentation

Reporting results of interest chiefly to the engineer

and the applied scientist. This section includes many

of the new developments in instrumentation resulting

from the Bureau's work in physical measurement,

data processing, and development of test methods.

It will also cover some of the work in acoustics,

applied mechanics, building research, and cryogenic

engineering. Issued quarterly. Annual subscription:

jDomestic, $2.75; foreign, $3.50*.

TECHNICAL NEWS BULLETIN

The best single source of information concerning

the Bureau's research, developmental, cooperative

'and publication activities, this monthly publication

;;is designed for the industry-oriented individual whose

daily work involves intimate contact with science

ijand technology

for engineers, chemists, physicists,

•^research managers, product-development managers, and

\,company executives. Annual subscription: Domestic,

! j$3.00; foreign, $4.00*.

•Difference in price is due to extra cost of foreign mailing. lOrder NBS publications from:

NONPERIODiCALS

Applied Mathematics Series. Mathematical

tables, manuals, and studies. Building Science Series. Research results, test methods, and performance criteria of building materials, components, systems, and structures. Handbooks. Recommended codes of engineering

and industrial practice (including safety codes) developed in cooperation with interested industries,

professional organizations, and regulatory bodies.

Special Publications. Proceedings of NBS conferences, bibliographies, annual reports, wall charts,

pamphlets, etc. Monographs. Major contributions to the technical literature on various subjects related to the Bureau's scientific and technical activities. National Standard Reference Data Series.

NSRDS provides quantitative data on the physical

and chemical properties of materials, compiled from

the world's literature and critically evaluated.

Product Standards. Provide requirements for

sizes, types, quality and methods for testing various

industrial products. These standards are developed

cooperatively with interested Government and in- dustry groups and provide the basis for common

understanding of product characteristics for both

buyers and sellers. Their use is voluntary.

Technical Notes. This series consists of communications and reports (covering both other agency

and NBS-sponsored work) of limited or transitory

interest. Federal Information Processing Standards

Publications. This series is the official publication

within the Federal Government for information on

standards adopted and promulgated under the Public Law 89-306, and Bureau of the Budget Circular

A-86 entitled, Standardization of Data Elements

and Codes in Data Systems.

CLEARINGHOUSE

The Clearinghouse for Federal Scientific and

Technical Information, operated by NBS, supplies

unclassified information related to Governmentgenerated science and technology in defense, space, atomic energy, and other national programs. For

further information on Clearinghouse services, write:

Clearinghouse

U.S. Department of Commerce

Springfield, Virginia 22151

Superintendent of Documents

Government Printing Offi^ce Washington, D.C. 2Qi02
U.S. DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20230

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

OFFICIAL BUSINESS