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Interrelations

between

Cement & Concrete

Properties

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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor,

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

Interrelations Between Cement and

Concrete Properties, Part 2

Sulfate Expansion, Heat of Hydration,

and Autoclave Expansion

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

Building Research Division

Institute for Applied Technology

National Bureau of Standards Washington, D.C.

Building Science Series 5

Issued July 1, 1966

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Contents

Page

Section 4. Variables associated with expansion in the potential sulfate

expansion test E. L. Blaine, H. T. Ami, and D. N. Evans 1

Section 5. Heat of hydration of portland cement

R. L. Blaine and H. T. Arni 27

Section 6. Variables associated with small autoclave expansion values

of Portland cements

R. L. Blaine and H. T. Arni 41
Section 4. Variables Associated with

Expansion in the Potential Sulfate

Expansion Test

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

The relationships between the chemical characteristics of 183 portland cements and

the expansion of mortar bars made of one part cement with 7.0 i)ercent SO3 and 2.75 parts

graded Ottawa sand were studied by computing multivariable regression equations with

the aid of a digital computer and determining which of the independent variables had a

significant effect on the expansion values. For cements containing 0 to 9 percent C3A, a

linear relationship appeared adequate whereas a higher power of the C3A content was

required with cements having 7 to 15 percent C3A. The principal variables other than the

potential C3A content associated with the expansion were the FeaOa content and CaO/SiOs

ratio. Of the other commonly determined variables, the loss on ignition, insoluble residue and K2O content were associated with high expansion values of the low C3A cements. Certain minor constituents or trace elements such as SrO, Cu, Cr, Ni, P, V, and Zn also appeared to be associated with the expansion values of the cements. The use of the

potential C3S content or the compressive strength of mortar cubes as variables indicated that high C3S was associated with cements having low expansion values as determined by

this test. CONTENTS

Page

1. Introduction 1

2. Materials 2

3. Testing procedures 2

4. Statistical treatment 2

5. Treatment of data 3

6. Results of tests 3

6.1. Results of preliminary examination 3

6.2. Expansion of low C3A cements at 14 days 6

6.3. Expansion of low C3A cements at 28 days 10

6.4. Expansion of low C3A cements at 84 days 10

6.5. Expansion of high C3A cements at 14 days 12

6.6. Expansion of high C3A cements at 28 days 12

6.7. Expansion of high C3A cements at 84 days 16

6.8. Tests on a supplementary series of cements 16

6.9. Autoclave expansion and sulfate expansion 16

7. Discussion 18

8. Summary and conclusions 24

9. References 26

1. Introduction

The ability of portland cement concretes to withstand the destructive action of waters or soils containing alkaline sulfates has been the subject of

many investigations, and there is extensive litera- ture on the subject [1, 2, 3, 4].^ The studies have

been made under both laboratory and field conditions, many of these in the development of test methods and specifications to assure satisfactory

performance of concretes exposed to severe or moderate sulfate action [5]

.

Although it is recognized that the cement content, water-cement ratio, and quality of the aggregate used in the concrete, as well as the curing, are important factors in determining the sulfate durability, it is also recognized that the cement composition, especially the potential tricalcium

1 Figures in brackets indicate the literative references at the end of this section.

aluminate content of the cement, is one of the major

factors associated with the durability of the concrete under these conditions. However, it has

been reported that [6] "We must look elsewhere

than to the aluminate for an explanation of the

^Tilnerability of concrete to sulfate solutions,'* and

[7] "There is some unrecognized factor in cement

which affects the sulfate resistance."

For lack of a satisfactory performance test yielding reproducible, definitive results within a rea- sonable time, it has been necessary in both Federal

[8] and ASTM [9] specifications to impose cer- tain chemical limitations on the cements intended

for use where sulfate resistance is a factor. Since

these specification limits were first adopted, a number of revisions have been made. In 1955 the

Working Committee on Sulfate Resistance of

ASTM Committee C-1 proposed a "Performance

Test for the Potential Sulfate Resistance of Port1
land Cements" [5]. One of the conclusions of the

report was "There is a relatively good relationship

between the 28-day expansion of the mortar prisms

and the performance of concretes exposed to sul- fate soils." It was also indicated, among other

things, that the proposed test method gave reproducible results which would discriminate between

different cements. This test procedure, therefore,

seemed to afford a means for determining some of

the variables associated with sulfate durability. Tests were therefore made on a number of the

cements which have previously been described [10,

11, 12], in an attempt to better determine the

variables associated with the expansions caused

by sulfates as determined by the proposed test method for potential sulfate expansion. In view

of previously quoted statements in this section [6,

7] relative to the inadequacy of the explanation of

the sulfate expansion solely in terms of pure compounds, consideration will be given to the possible

effect of the minor and trace elements present in Portland cements.

2. Materials

The frequency distributions of results of chemical analyses as well as spectrochemical analyses

of the Portland cements used in the study have

previously been reported in part 1 of this series of

articles [10, 11, 12] dealing with materials and

techniques employed and the occurrence of minor

and trace elements in portland cements. The test for potential sulfate expansion was made on 183

Portland cements. These cements are believed

fairly representative of the portland cements of

the different types manufactured in the United

States.

3. Testing Procedures

The testing procedures used followed closely

(with a few exceptions as will be noted later) the

recommendations of the Working Committee on

Sulfate Resistance of ASTM Committee C-1 on Cement and the proposed method of test as originally published [5]. This method consisted of adding sufficient gaging plaster to the cement to make

the SO3 content 7.0 percent by weight of the ce- ment. The 1:2.75 (cement-plaster to graded

Ottawa sand) mortar was mixed in a mechanical

mixer with the required amount of water.^

The plastic mortar was molded into 1 X 1 X 10

inch effective-gage-length prisms and cured in a moist cabinet at 95-100 percent relative humidity

for 24 hours, after which the molds were stripped

and the length of the prisms measured. Tlie speci- mens were stored in water and length measure- ments were made at 7, 14, 21, 28, 56, and 84 days

from the time of molding. Additional measure- ments were made at monthly intervals for 1 year

on specimens which had not warped, disintegrated, or been accidentally broken in handling. The

testing procedure used deviated from the proposed

testing procedures in that only three instead of

six speciments were molded for each of the cements. The reduced number was possible because a special plastic tape was used to line the molds which

facilitated the release of the specimens and reduced

breakage. The expansion values expressed as a percentage increase in length based on the 24-hour

measurements were the averages of the three speci- mens. However, when only two specimens re- mained intact after removal from the molds, their

average expansion was used in future calculations.

All specimens were made by one operator in one

laboratory.

Supplementary tests on 21 portland cements

(not included in the original series) were made us- ing duplicate sets of three specimens on different

days to evaluate the precision of the test results.

4. Statistical Treatment

The statistical treatment of the data used has

been described in detail in a previous article [10].

Plots were made of the expansion values at 14,

28, and 84 days versus various independent variables, and equations were computed with different

combinations of independent variables in order to find those combinations which resulted in the best

^ The combined proportions of dry materials mixed at one

time consisted of 400 g of cement and gypsum molding plaster combined and 1100 g of graded standard sand. The quantity of mixing water used was as follows : For types I. II, IV, and V cements 216 ml For types lA and IIA cements 208 ml For type III cement 224 ml For type IIIA cement 216 mi

(The present requirement that an amount of water shall be used

such that the mortar shall have a flow of 100 to 115 percent was

not in effect at the time these tests were made.)

fit attainable of the data to the computed relationship. The various exploratory techniques described in part 1, section 1 were used to determine

which of the available independent variables

should be tried in the equations and those independent variables which had "coefRcient/s.d." ^ values less than one were deleted from computa-

' The following statistical terms are used in this section : S.D. = Estimated standard deviation calculated from the de- viations from the fitted equation, or the estimated stand- ard deviation of a single observed value of a variable.

s.d. = Estimated standard deviation of the coeflicient of an

individual independent variable used in a fitted equation.

Coef./s.d. or coefBcient/s.d. = ratio of the estimated coefficient (of an independent variable used in an equation)

to its estimated standard deviation. "F" = Fisher's ratio of variances. Critical "F" values were

obtained from tables presented in textboolcs on statistics. A more complete discussion is presented in the first section on

"Materials and Techniques".

2
tions of subsequent equations. As in the previous

article [11] both commonly determined variables

and the minor constituents were employed in order

to determine their possible effect. A discussion of

the limitations of the statistical treatment has

previously been presented [10].

5. Treatment of Data

The maximum specification limits of 5- and 8- percent tricalcium aluminate (C3A)* for sulfate- resisting and moderate-sulfate resisting cements,

respectively, have been in effect since the time of

the development of specifications for the five types

of Portland cement ( 1930-1940) . There have been some uncertainties with respect to these limits. Plots of sulfate expansion versus C3A have, for

example, generally indicated a "break" in the curve

in the 7- to 9-percent C3A region. This was also true in the present study, but there was no obvious

corresponding break at the 5 percent C3A specification limit. It therefore appeared desirable to com'bine the sulfate-resisting and moderate-sulfate- resisting cements into one group and include

also those cements having up to 9.0 percent C3A.

For cements which were not classified as sulfate

resisting it appeared desirable (because of the uncertainty of the value differentiating the cements

with respect to moderate sulfate resistance) to include cements having 7 to 15 percent C3A in a second group. Separate calculations were made on

each of the two overlapping groups of cements

with 0 to 9 and 7 to 15 percent C3A, respectively.

There were so few cements below the 5-percent

specification limit for sulfate-resisting cements

that equations developed for these cements alone

would have been of no significance.

Although the expansion measurements were made at regular intervals up to one year, it appeared from plots of expansion versus age that

the resulting lines for the different cements did not

cross each other to any great extent at the early

ages. Therefore computations were made for the

expansion values only at 14, 28, and 84 days.

The nomenclature and abbreviations used in the

previous section [10] are also used in this section.

In addition, SE14, SE28, and SE84 are used to indi- cate the percentage expansion of the prisms at 14,

28, and 84 days, respectively.

6. Results of Tests

6.1. Results of Preliminary Examination

The frequency distributions of the cements with

respect to expansion of the prisms at 14, 28, and 84

days are presented in tables 4-1, 4-2, and 4-3, re- spectively. It may be noted that with each of the

types of cements, as classified, a considerable range

of expansion values was obtained. Cements classified as types I and lA had the greatest range of

values at all ages, and their ranges overlapped the

ranges of values obtained with cements classified as types II, III, IV, and V [8, 9]. The cements

Table 4-1. Frequency distribution of cements with respect

to expansion of prisms in the potential-sulfate-expansion test

Percentage expansion at 14 days

Type cement Oto 0.020 0.040 0. 060 0. 080 0. 100 0. 120 0. 140 0. 160 0.020 to to to to to to to to Total

0.040 0.060 0. 080 0. 100 0. 120 0. 140 0. 160 0. 180

Number of cements

I 13

19

141

110

35

2

1

16

3

1

4

1 41

1 1 1 75

8

16

1 48

118

1 15

lA

II* 5 IIA*

11 1 6 IIA

Ill 1 5 2 IIIA 1 IV, V 4 9 2 Total 11 85 51 23 5 5 1 1 1 183

Classified as type I and lA when procured.

Table 4-2. Frequency distribution of cements with respect

to expansion of prisms in the potential-sulfate-expansion test

Percentage expansion at 28 days 00

0

1

000 00 s? Type 0 0 CO Total cement d d d d d cS d d d 0 0

0 0 0 0 0 0 0 0 0 0 0 0 d

0 0 0 0CO 000 0 0CO 000 0 g 0 0 0 tH »H 0 d d d d d d d d d d

Number of cements

3 11 24 13 10 3 4 3 1 1 2 75 lA 2 1 3 1 1 8

II*. 2 9 4 1 16 IIA* - 1 1 II.... __ 21 24 3 48 IIA_ 1 1 Ill 9 2 3 3 1 18 IIIA 1 1 rv, V 13 2 15 Total

2 65 47 31 19 13 3 5 3 2 1 2 183

'Classified as type I and lA wlien procured.

The nomenclature customary in cement technology, viz, C3A,

CsS, C2S, and C4AF, refers to the potential compound composition,

tricalcium aluminate, tricalcium silicate, dicalcium silicate, and

tetracalcium aluminoferrite, respectively, as calculated by

standard procedures presented in both Federal and ASTM speci- fications l;or Portland cements. The letters C, A, F, and S may

sometimes be used in referring to CaO, AI2O3, Fe208, and SiOa, respectively, as in the ratios A/F and S/(A-fF) and C/S. In the C/S ratio, the CaO was corrected for the amount of CaO

combined with the SOa- Other abbreviations include NAE for non-air entraining ce- ments, AE for air-entraining and AE-|-NAB for air-entraining

plus non-air-entralning cements, APF or Air P. Fine, for fine- ness in square centimeters per gram as determined by the air permeability method, and Wagn. or Wagn. Fine, for fineness in square centimeters per gram as determined by the Wagner turbi- dimeter method. Also used were Loss for loss on ignition, Insol. for insoluble residue, and Alk for total alkali expressed in terms

of percent NazO. (Total alkalis %Na2O+0.658% K2O.) The

values were determined by standard procedures.

3
SULFATE

EXPANSION INDEPENDENT VARIABLES

AGE NOTE Si O2 AI2O3 FegOs CnO MaO SO3 NaaO KzO TOTAL

ALKALI C,A c,s CoS C4AF A

F A+F

AIR,P, FINE WA6N

FINE. AIR

1:4 MOR

14 days

(I)

(2)

(3)

(4) NL

-19 NL +24 LZ

NL

-15 L?

-2 NO

+ 1 L? H6

L? + 10 NL + 16 NL + 12 NL +24NO -5

L?

-13 NL

-14 NL + 24 NL

-18 NO

+ 2 L? -15

L? + 8

28 days

(1)

(2)

(3)

(4) NL

-19 NL

+ 24 NL

-19 L? -6

NO

+ 3 L? +20 NO+ 6 NL+-I9 NL + 16 NL + 24 NO -7

L?

-15 NL +20

102

NL L?

-16 -2

L?

-12 L?-1-24

84 days

(I)

(2)

(3) (4) NL

-19 NL +24

NL

-18 NO

-I NO + 2 NL + 24

LP + 6 NL + 19 \±

NL +19 LZNL + 24

LP -2 NL -20

NL

- 14 NL

+ 24

102

NL NO

-18 -2

LP L?

+15

Figure 4-1. Results of plotting sulfate expansion on the "Y" axis versus independent variables on the "X" axis.

(1) Ratio of number of plotted points occurring in parts of diametrically opposite quadrants. (High ratios indicate significant relationships)

.

(2) General trend of line drawn through plotted points.

(3) Apparent nature of relationship, L=linear, NL = non linear, NO = no apparent relation, N? = nature of relationship not

determinable.

(4) Quadrant sum. (absolute value of 11 or greater indicates a relationship at the 95% probability level. See ref. 10).

formerly classified as types I or lA but later classifieci as type II or IIA in the revised specification

had, with one exception, expansion values in the same range as cements classified as type II in the

earlier specifications. Most of the cements classi- fied as type III had low expansion values at 14

days, but at 28 and 84 days the values of the different cements of this type were more widely

scattered, and at 84 days two of them exceeded the

median for type I cements. In figure 4-1 are presented the results of plotting

the expansion of the prisms at 14, 28, and 84 days on the y axis versus various independent variables on the X axis. The ratios in lines ( 1 ) and the numbers in lines (4) of the figure are the result of two

methods of checking for random scatter of plotted

points. A high ratio in line ( 1 ) indicates a high

degree of correlation, or lack of randomness. In

line (4) a quadrant sum with an absolute magnitude equal to or greater than 11 (24 is the maximum possible) indicates a significant relationship

at the 95 percent probability level. The method

of obtaining these figures and their meaning are described more fully in part 1 [10] . High values

for AI2O3, C3A, and A/F ratio were associated

with those cements having high expansion values.

To a lesser degree, the higher values for total al- kali, K2O, SO3, and the air content of the 1 :

4

mortars also appeared to be associated with those

cements having high expansion. It may also be

noted that high values for Si02, FegOs, C4AF, C2S,

S/(A + F), and Wagner fineness appear to be asTable 4-3. Frequency distribution of cements with respect to expansion of prisms in the potential-sulfate-expansion test

Percentage expansion at 84 days

Type cement

0

to

0.020

0.020 to

0.040

0.040 to

0.060

0.060 to

0.080

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

0.250

0.250 to

0.300

0.300 to

0.350

0.350 to

0.400

0.400 and Over

Total

Number of cements

I 1 6 7 4 8 8 4 4 10 7 7 1 8 75 lA 1 1 1 2 2 1 8

II* 5 5 1 4 1 16 IIA* 1 1 II 1 16 23 6 1 1 48 IIA 1 1 III 2 6 2 2 2 1 1 2 18 IIIA 1 1 IV, V 5 7 2 1 15 Total —- 13 35 36 22 7 11 10 6 4 12 9 8 1 9 183

'Classified as type I and lA when procured. 4
0.30

o 0.10 <

0.00 -

0. 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0

7o C3A

Figure 4-2. Results af plotting the percentage expansion at 14 days versus the potential tricalcium aluminate content of the portland cements.

0.30

0.20 -

0.10

0.00

1.5 3.0 4.5 6.0 7.5 C3A

9.0 10.5 12.0 13.5 15.0

Figure 4—3. Results of plotting the percentage expansion at 28 days versus the potential tricalcium aluminate content of the portland cements.

sociated with cements having low expansion values.

In general, the plots for an independent variable

at the different ages were similar and the quadrant sum values [10] were about the same, irrespective

of age. The results of plotting all values of sulfate ex- pansion for 14, 28, and 84 days versus C3A content

are shown in figures 4-2, 4-3, and 4-4, respectively.

(These plots were made by the computer-printer

and many of the dots represent more than one

plotted point. Thus the concentration of values

in some regions is not clearly indicated.) Certain

cements, as will be indicated later, were not in- cluded in these plots. It may be noted that al- though thero appears to be a fairly good relationship between the expansion values and the potential C3A content, the band is rather broad in

that a given expansion value is associated with

cements having a considerable range in C3A content, or with a given potential C3A content a range

of expansion values is obtained. It may also be

noted that the relationship for cements of 0 to 9

percent C3A appears to have a much lower slope

than that for cements above the 7 to 9 percent

C3A range, especially at the later ages.

It was apparent in computing a variety of trial equations that some of the cements always had

large deviations from the computed values. One

of these cements had a high autoclave expansion

(5.5 percent), with an MgO content of 1.4 percent.

This cement also failed to meet the 28-day compressive strength requirement. Another cement

had a 24-hour compressive strength of only 120 psi

and also failed to meet the 3- and 28-day strength

5
0.50 -

0.40

00 0.30 -

0.20 -

0.10

0.00

0. 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0

Figure 4-^. Results of plotting the percentage expansion at 84 days versus the potential

tricaldum aluminate content of the portland cements.

requirements. A third cement also had a larger

expansion than would be expected for its C3A content. This cement had a high Zr content, of the

order of 0.5 percent, and a relatively low 1-day

compressive strength. Although these cements as well as the three white portland cements were used

in preliminary computations and in the graphs of

figure 4—1, they were not used in the final equations

presented in this section nor in figures 4-3,

and 4-4. The white portland cements were not in- cluded because of the low Fe203 content as compared to other portland cements. Preliminary

plots indicated that the expansion values of the

white Portland cements were higher than" for other

cements of comparable potential C3A content. This confirms a previous report [13] which indicated that the reactions involved with white portland cement are different from those of other cements.

6.2. Expansion of Low C3A Cements at 14 Days

In table 4-4 (p. 7) are presented coefficients for

equations relating the 14-day expansion of the

prisms of the cements having 0 to 9 percent C3A to various independent variables. The S.D. values

with C3A or AI2O3 as the sole independent variables obtained for equations 1 and 2 for AE + NAE

cements and equations 8 and 9 for the NAE

cements were significantly lower than the S.D.'s

for the expansion values of groups of cements as indicated in the footnotes 1 and 2 of this table. (In this and other instances where a relationship is said to be significantly improved in the second of

two equations by the inclusion of one or more additional variables, refer to table 4—20 where ratios of

variances for the reduction in error variance are

given. See also the discussion in part 1 of this

series.) Chemical limitations of C3A, C3S, AI2O3,

C4AF, Fe203, and Si02 have all been employed in

specification requirements for sulfate-resisting cements. Equations 3 and 10 using these variables

have lower S.D. values than when C3A or AI2O3 are used as the only independent variable. However,

the coefficient/s.d. ratios of three of the five inTable 4-5. Calculated contributions of independent vari- ables to 14-day sulfate expansion of cements having 0 to 8

percent C3A

Values Coeffi- Calculated Independent used for cients from Calculated con- range of variable independent equation tribution to SE14 contribuvariable 12, table t-4 tion to SEu

Const. =-1-0. 042 C3A 0-8 -1-0. 004 -1-0 to -1-0. 032 0.032 Fe203 0-5.5 -1-0. 007 -i-0 to -f0. 038 0.038 CaO/SiOz 2. 4-3.

3

-0. 025 -0. 60 to -0. 082 0. 022

Insol 0-1.0 -0. 013 -1-0 to -0.013 0. 013 Loss _ 0-3.0 -fO. 003 0 to -f0. 009 0.009 K2O 0-1.0 -1-0. 010 0 to -hO. 010 0. 010 SrO 0-0.4 -1-0. 012 0 to -1-0. 005 0.005 Cu 0-0.05 -0. 150 0 to -0.007 0. 007 V 0-0.1 +0. 054 0 to -1-0.005 0. 005 Zn 0-0.2 -1-0. 021 0 to -1-0. 004 0.004
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= 8 gg gg go gg So oo o o o o oo oo oo oo o o o o

o S o S o c oo

I ^

o o oo

(MCO »CO GO-^ M CO CO O i- Oi O Oi »0 CD CD Cisco lO Ci oo oS oS oS oS oc o o

I ^

^9Q 03

Tj< o ao i-t 00

CO -^00 COOO (N gg ig gg gg

ocD oc5 oo oo

- CO CO

& O 00 CO

I

o o

o o 88 3800 00 00

eo Tf* §8

o ci

CO T-t 88

SS 88

ci 00

00 CM TP CO OCO 1—I 00 00 1-H CD 1-H Oh-h CO "-H t-* 00 .-H 00 1-H Ol r-I O tH CM Oi T-t T-H (N 1-H ,-H 88 88 88 S8 88 88 88 88 88

00 00 00 00 00 00 00

O M OJ o 88

00+^ 00

S8

00 00 o o 380<3

00 00 00

00

88

o o

lO CO S8

00+-

II II

CO TP

*p o S8

II 11

O ^ 1-H 00

CO 1-H r-J 00 00

II II

o o

11 II 00 00

O 00 OS CO 52 00

OS CO CO O 00

c5 CO CO CO 00 o c5 00

o o

II II 00 00

§ II II > II II 00 o o

II II

S 00 o o

o o +'-'

II II 00II II

+
1-< ^^ ^ rS

.-I i-H «o coco r^to ^ I to CO C3 CD o o o o o o o o

oo oo So So

oo do do dd +^ I -

O Tt< CO to d d dd

dd d d

o o o o d d d d

o^ o§ o§ oo oS oS o^ o§ oo

dd dd dd dd dd dd dd dd dd dd +^ +'-' +^ +^ +^ +^ +^ +^

is ii is is ss is is is is is

dd dd dd dd dd dd dd dd dd dd +'-' +^ +^ +^ +^ +^ +^ +^ +^

TfS" i>.5? coco coco cot', ic .—I lo If co' cocJ g lO CO g coco ^- ^ ^® »0 CO ^ oo oS oo oS oo oS oo oS oS oo dd dd dd dd dd dd dd dd dd dd 1^ 1^ I"" I"" 1^ 1"^ 1^ 1^ I"" I"" CO^ »C O^H iO O eO»C i-H if? o^ oco t- c^o fO« (M CO CM CO I-H CO CO f-H o CO 00 CO 00 M 00 coco coo coo coo coo 03'^ CO<-H coo coo CQO CO o oo oo oo oo oo oo oo do oo do

dd|w dd dd dd dd dd dd dd dd dd 1^ 1^ ,w |w ,w jw |w ,w 1^

S2

SS

r^Oi »n CO o CO r— co o «o 00^ gi cow ss ss ss ss >g gg gg gg gg gg

oo oo oo oo oo oo

1^ +~-' +^ +^ +^ oo oo oo oo oo

oo oo

CO w OS is is

oo oo

CM r~

CO —( ss

dd

is

oo

F-( iC O CO CO

o o oo o o

oo oo

CO O ss

dd o o

CO CO ss SS 2§ o o

O Oi BS

I-H Oi

CO 00 (N ss ss

» ^ r» 00 ^ c o o +-

II II

o o

1

II II ooII II oo+^II II

an

oo oo

II II oo oo oo o o oo ooII II

o o
dependent variables used in these equations were

less than one. The potential C4AF values were

not used as they are computed as a constant times

the FejOs values. These equations also are af- fected by the interaction of C3A, AI2O3, and FeaOa,

since the ALOs and FeaOa values are both used in calculating the potential C3A values.

Using commonly determined independent variables as indicated in equations 4 and 6 as well as

in equations 11 and 13 resulted in large reductions

in the S.D. values as compared with those obtained

in equations 1 and 2 or in 8 and 9, respectively.

The use of additional minor constituents or trace elements indicated in equations 5, 7, 12, and 14

also resulted in further significant reductions in

the S.D. as compared with equations 4, 6, 11, and

13, respectively. Various other independent variables were used in equations but none of them

resulted in a better fit to the computed relationship.

Using values of 0 to 8 percent C3A and approximate ranges of the other independent variables

as presented in part 1, sections 1, 2, and 3 [10, 11,

12] and the coefficients from equation 12 of table

4-4, the calculated contributions to the percentage

expansion of the prisms are presented in table 4-5.

A value of 8 percent C3A was used in this table

as well as in tables 4—7 and 4-9 inasmuch as it is the upper specification limit for moderate sulfate

resisting cement. For cements not considered sul- fate resisting, a value of 8 percent was used as the

lower limit as in tables 4—11, 4—13, and 4-15. Also

presented in this table are the calculated rangas

of the computed values. Some of the limitations

of such computations and values have previously

been discussed (10).

6.3. Expansion of Low C3A Cements at 28 Days

In table 4—6 are presented coefficients for equations relating the 28-day expansion of the mortar

prisms of cements having 0 to 9 percent C3A to various independent variables. Again it may be

noted that with the use of C3A or AI2O3 as the sole independent variables, the S.D. values for equations 1 and 2 or 14 and 15 were significantly

smaller than the overall S.D. for expansion values

alone (see footnotes in table 4^6). Equations 3

and 16 illustrate the results obtained when com- monly specified variables are employed as independent variables. When other commonly determined independent variables were used as in

equations 4 and 10 for the AE + NAE cements or equations 17 and 23 for the NAE cements, the S.D.

values were significantly lower. When minor or

trace elements were included with the commonly

determined independent variables as indicated in equations 6 and 12 or 19 and 25, the S.D. values were again reduced significantly. It may be noted

that V and Zn had coefficient/s.d. ratios greater

than one in the equations for the 14-day-expansion

values (table 4-4). With 28-day expansion, however, these two variables were not significant and

Table 4-7. Calculated contributions of independent variables to 28-day sulfate expansion of cements having 0 to 8

percent C3A

Values used Coefficients Calculated Independent for inde- from equa- Calculated contri- range of variable pendent tion 19, bution to SE 28 contribuvariables table 4-6 tion to SE28

Const. = +0.055 C3A 0 -8 +0. 0061 0 to +0. 049 0.049 Fe203--- 0 -5.5 +0. 0087 0 to +0. 048 0.048 CaO/SiOi!-- - 2. 4-3. 3 —0. 0329 —0. 079 to —0. 109 0. 030 Insol 0 -1.0 -0. 0153 0 to -0. 015 0.015 Loss.- 0 -3.0 +0.0046 0 to +0. 014 0.014 K2O 0 -1.0 +0. 010 0 to +0. 010 0.010 SrO - 0-0.4 +0. 019 0 to +0. 008 0.008 Cu.-- —- 0 -0.05 -0. 13 0 to -0. 006 0.006 Ni 0 -0.02 +0. 51 0 to +0. 010 0.010

were replaced by Ni in the 28-day expansion equations. Equations 8 and 9 as well as 21 and 22

(table 4^6) illustrate the effect on the coefficients and s.d. values when using only the "odd" or "even" cements in the array as compared to the

coefficients and s.d. values obtained when using all the c«ments as in equations 7 and 20, respectively.

The extent of agreement of the values computed

for the two groups of cements indicated to some

extent the confidence which could be placed in the

coefficients of the different variables in the equation. When (CsA)^ was used instead of C3A

or (ALOs)^ instead of AI2O3, the S.D. values

obtained were lower in every instance. The use of

other independent variables did not cause any appreciable reduction in the S.D. values.

Using values of 0 to 8 percent C3A and approximate ranges of the other independent variables

as previously determined together with the coeffi- cients from equation 19 of table 4-6, the calculated

contributions to the percentage 28-day expansion

of the prisms are presented in table 4—7. Also

presented in this table are the calculated ranges

of the computed values for the various independent

variables.

6.4. Expansion of Low C3A Cements at 84 Days

In table 4r-8 are presented coefficients for equations relating the 84-day expansion of the prisms

of the cements having 0 to 9 percent C3A to vari- ous independent variables. As in the equations

developed for the 14- and 28-day expansion, the

use of certain commonly determined independent

variables resulted in a large decrease in the S.D.

values, and with the use of certain minor or trace elements, a further significant decrease in the S.D.

values was attained. Also, as in equations developed for the 28-day expansion, the use of

(C3A)^ resulted in slightly lower S.D. values than was obtained when C3A was used.

Presented in table 4r-9 are calculated contributions of the various independent variables to the

percentage expansion at 84 days together with the

calculated ranges of the computed values. These

values were computed on the basis of the coeffi10
00 00 o o lO CD

?5 5!? o o o o o" o o o o o o o O o o o O o d d d d

rH O

+-'

CM O M do

I ^

00i-tOS O CO .-HO

CO Tji CO d d

I ^

1-1 Ml o

i-H O

OS CO OS CO d d do

i£5 C) Oi O CO

.-H d

o o

o o

CO »o COo o d d d d o o +-'

CO M c5 o do d d

oo

d d

to CS 00 r-- 00 CO t-. (NO (Si o O O O o OO o o OO o o oo

OS CO

c5 o

M O CO o »o o 00 CO ^ qp ^ o o OO OO o.o o o

OO

do

OS I - ssOOoo

o o

do*

»o CD --I o o o o o o

C3S CD sso o oo o o oo

J OS CO IS is ss oo oo o o oo oo+-' oo

CD O 00 !M

1-H oo

d d

COCO --I oo

d d

00 --I (N OS 00

1—I ^ CD rH CO --H (M 1-H o o o o

coco

1-H C4 f-H oo

(M I-H oo

dd

I ^

O .-H o o

d d

I

0265

0117) W CO op

eg iT-i CO CO

»C -H o o d o o o do

1 ^ d d

1 d d

1 d d1 ^

00 oto

1-H rOS lO CD o oTjH ,-1 CO OS

OS iC I-^ Tt<

,-H "^^H I-H o o o o

CD^1-1 IC I-H o o o o oo

I ^ o o oo

I ^

CO "O o o So So So So So

o o

I ^ oo

I-H CD I-H Tt<

.-H CO 1-H oo 1-H o o o o

*C0

(M (N

rH O o o

c5 (N

r-H O O O

o o oo oo o o o o oodd

CDCD

1-H CO 1-H CNJ M CSI OO

O I-H O 1-H Q O O O O O

d d d d

t-H CS CS

1-H O T-H O O O

OS ^ »0 I-H t— CS CS o o ooo o

o o oo o o o o

I ^

to CS o o oodd

I ^ o o

o o odd

I-H CO

I-H O oo

oo

I ^

CO CO

00 CS o o

o o

I ^ ooI ^

CD CO lO CO CO o CO d o o o o

o o d d oo o 5

dd dd

oodd o o

o oo dd o o

00 OS

OS o ooodd oo

lO o §3o o

d d oodd

o o dd oo o o oo o o o o o o

o o

II II

o o

CS lO I-H CD O OS rH So So

d d d d

II II II II

00 CD OS Tt< O O

II 11

o o

1-H O dd

oTt< CO

t- CO o o

CS CO OS 00

CO 1-H 00 O S in S

d d d d

CS CO d d

TJH 00 Tt* CO CO

rH O CO O

o o

o o

d d +^

II.

II

CS OS CO o o

^ o

«0 1-H oo

d d +^

'I

II

CO «

CO o CO oo ^o

lO »0 CO 00 CO ^~-Tt< CS OS t— 2g

o o o o oo

II II

o o oo

o ^ o

d d

II II Si

o o

+

<!

11
Table 4-9. Calculated contributions of independent variables to 84-day sulfate expansion of cements having 0 to 8

percent C3A

Values used Coefficients Calculate^ Independent for Independ- from equa- Calculated contri- range of variable ent variable tion 19, bution to SEai contributable 4-8 tion to SE84

const. = -t-u. u/1 C3A - 0 -8 -\-0. Oil 0 to -t-u. 088 0. 088 FeaOs 0 -5.5 -1-0. Oil 0 to -1-0. 061 0.061 CaO/Si02 2 4-3.3 —0 046 —0.101 to —0. 152 0. 051 Insol - - 0' -1.0 -0. 026 0 to -0. 026 0.026 Loss - 0 -3.0 -1-0. 005 0 to -f0. 015 0. 015 K2O - 0 -1.0 +0. 019 0 to +0. 019 0. 019 SrO 0-0.4 -1-0. 045 0 to -1-0. 018 0. 018 Cu 0 -0.05 -0. 197 0 to -0. 010 0. 010 Nl 0 -0.02 +1. 131 0 to +0. 023 0.023

cients obtained in equation 19 of table 4-8 together

with the ranges of the independent variables as previously determined.

6.5. Expansion of High C3A Cements at 14 Days

In table 4-10 (p. 13) are presented coefficients for equations relating the 14-day expansion of

prisms made of cements with 7 to 15 percent C3A

to various independent variables. Equations 1 through 6 were computed using the AE + NAE

cements and equations 7 through 12 for the NAE

cements only. Preliminary trial equations indicated that the second or third power of the C3A

values resulted in lower S.D. values than when the

first power was used with the cements having 7 to 16 percent C3A. Equations 1 and 7 indicate that

the use of (C3A) - by itself caused a large reduction

in the S.D. values. As indicated by equations 2

and 8, an increase in C3S was accompanied by a reduction in expansion of the prisms, and inclusion of this variable reduced the S.D. values significantly. When the other commonly determined

variables were included as in equations 3 and 9, the S.D. values were further reduced significantly.

The use of the minor constituents or trace elements,

SrO, Cr, and V, as in equations 4 and 10 appeared

to produce a further small reduction in the S.D.

values. However, the coefficient/s.d. ratio for

loss on ignition was reduced to less than one when

these elements were included, and therefore loss was eliminated from the equation. Equations 5 and 6 as well as 11 and 12 using (Al203)^ resulted

in approximately the same S.D. values as were

obtained using (CaA)^ for equations 3, 4, 9, and

10, respectively. The loss on ignition had a coefficient/s.d. ratio greater than one in the four

equations using (AlaOa)^ values. With the use

of the trace elements, SrO, Cr, and V, S.D. values were not significantly reduced.

Using squared values of C3A for the cements

with 8 to 15 percent C3A together with the approximate ranges of the other independent variables and with the coefficients of equation 10 of

table 4^10, values were calculated for the contributions of the independent variables to the perTable 4-11. Calculated contributions of independent variables to 14-day sulfate expansion of cements having 8 to 15

percent C3A

V alues uoem- Calculated

inclBpenaent used for in- cients from Calculated con- range of variable dependent equation tribution to SE14 contribuvariable lu, taDie4^iu tion to SEi4

Const. =-|-0. 1046 (C3A)2 64-225 +0. 00047 4-0. 030 to -t-0. 106 0.076 Fe203 0-6.5 4-0. 0049 0 to -f-0. 027 0.027 CaO/Si02 2. 4-3.

3

-0. 0392 -0. 094 to -0. 130 0.036 SrO 0-0.4 -0. 0392 0 to -0. 016 0.016 Cr 0-0.02 +0. 5263 0 to -f-0. Oil 0.011 v 0-0.1 -0. 2491 0 to -0. 025 0.026

centage expansion of the prisms. These values

are presented in table 4—11 together with the cal- culated ranges of the computed values.

6.6. Expansion of High C3A Cements at 28 Days

In table 4-12 is presented a series of equations

relating the 28-day expansion of the mortar prisms

of cements having 7 to 15 percent C3A to various

independent variables. The use of (CaA)^ in

equations 1 or 14 or (AljOs)^ in equations 10 or 23 resulted in a large reduction in the S.D. values.

Comparing equations 2 with 3 or 15 with 16, it may

be noted that the use of the potential C3S content alone resulted in the same S.D. value as the use

of a number of commonly determined independent

variables. This was true for both the AE + NAE

and the NAE cements. By including certain

minor constituents or trace elements the S.D.

values were further reduced to a significant degree as may be noted by comparing the S.D. values

of equations 3 and 4, 11 and 12, 16 and 17, or 24

and 25. The use of (ALO3)' in equation 10 (for AE

+ NAE cements) and in equation 23 (for NAE

cements) resulted in a higher S.D. than the use of

(CsA)^ in corresponding equations 1 and 14. However, when FegOs, CaO/Si02, and three of the

trace elements were included (equations 8 and 12

for AE + NAE cements and equations 21 and 25

for NAE cements) the S.D. was the same whether

(AI2O3)- or {CiAY was used. The use of C2S

and S/(A + F) in place of C3S alone (other variables remaining the same) produced the same S.D.

as indicated in equations 7 and 9 or 20 and 22. In trying many combinations of variables (for

many of which trials the equations are not produced here) the suspicion arose that there was an

interaction between some of the trace elements and

calculated compounds or oxides. This means that

the effect of one variable depends on the level of

another variable which interacts with it. This

is shown in table 4-12 by the results when the products C3A X V and AI2O3 X V are included (equations 7, 9, and 13 for NAE + AE cements and 20,

22, and 26 for NAE cements). For AI2O3 X V,

for example (equations 12 and 13), S.D. is decreased significantly and the ratio coefficient/s.d.

for the product term is appreciably greater than

12
si

6

>

-0.2885 (0.

1327)

-0.

2212

(0.

1404)

-0.

2491

(0.

1377)

-0.

1880

(0.

1453)

o

+0.

5751

(0.

2830)

+0.

6154

(0.

2805)

+0.

5263

(0.

2914)

+0.

5549

(0.

2900)

SrO

-0.

0181

(0.

0137)

*

-0.0117 (0.0135)

-0.

0392

(0.

0143)

-0.

0213

(0.

0142)

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coco CO (M-^ o -g* lOCO OO QO OO rH O oo oo oo oo oo oo oo oo

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o o

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I ^

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c= o +-'

lO CO lO CO

00 CM

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CO o(M o o o o

o' <r5 o o

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CM O oo o o

I ^

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c3o CDC) oo oo +^ +^ +^ +^

cp O CO o o o o o O Q O O

CD O O O O o o o o

OSCO O o ooo

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CO CD OS

t- o o o o 88 88

o o o o o o o o o o o o oo

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i-t O w i« O I-H o

^ CO o o o o o o oo

1-H (M OS CO

I-H CM o o

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Si o o

CDO

eo

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c5c5

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t - 00 O 1-H o o oo oo oo oo

1 ^ 1^

II II II II II li II. !L

1'. II II oo

208-577 O—6( 3 15
Table 4-13. Calculated contributions of independent variable to 28-day sulfate expansion of cements having 8 to 15

percent C3A

V dlUCiS Coeffi- C &lciil3.t6d used for in- cicnts from Calcul&tcd conV CU let UK> d6p6Ild6Dt 6QU£lti011 tribution to Sfjjs contribU"

V m id uic tinn tfi STT.fto

Const. = +0. 092 (C3A)2._ 64 -225 +0. 00079 +0. 052 to +0. 178 0.126 FejOs 0-6.5 +0. 0056 0 to +0. 031 0. 031 CaO/SiOz 2.4- 3.3 -0.04 -C. 096 to -0. 132 0. 036 Cr 0 - 0.02 +1.1 0 to 1-0. 022 0.022 V 0-0.1 -0. 44 0 to -0. 044 0. 044 P 0-0.5 -0. 07 0 to -0. 035 0.035

2. Also, note that the coefficient for V changes

from -0.5 (s.d. 0.2) to +4.3 (s.d. 2.0) while all the rest of coefficients and s.d.'s in the equation

change very little. This indicates that there is a

correlation between AI2O3 and V and that the

effects of these two variables are not simply additive. The changes are significant also for the NAE

cements (equations 25 and 26). There is some

indication that the same situation holds for C3A

and V (equations 4 compared to 7 and 17 compared

to 20) , but the change in S.D. in this case was not

large enough to be significant.

Using the squared values of 8 and 15 percent

C.3A together with the approximate ranges of the

other variables and the coefficients of equation 21

of table 4—12, the calculated values for the contributions to the percentage expansion of the prisms

at 28 days are presented in table 4^13 together with

the calculated ranges of the computed values.

6.7. Expansion of High C3A Cements at 84 Days

In table 4-14 (p. 17) are presented cofficients for

equations relating the 84- day expansion values of

the prisms of the cements having 7 to 15 percent

C3A to various independent variables. The S.D.

values using (CsA)^ or (AlgOs)^ as independent

variables as indicated in equations 1 and 8 for

AE + NAE cements or 11 and 18 for the NAE

cements were significantly lower than the S.D. val- ues for the respective cements. The use in the

equations of the CaO/SiOz ratio with the (CsA)^

or the CaO/Si02 ratio and FeaOg with the

(AI2O3)* variable resulted in a significant reduction in the S.D. values as may be noted in equations

3 and 9 or in equations 13 and 19. The use of cer- tain minor constituents as in equations 4 and 10 or

in 14 and 20 resulted in further significant reduction in the S.D. values. The coefficients for the

independent variables obtained when the "odds"

and "evens" in the array of cements were computed

separtely are presented in equations 5 and 6 for the

AE + NAE cements and in equations 15 and 16

for the NAE cements. Using the third power of the values of C3A for

cements with 8 to 15 percent C3A together with the

approximate ranges of the other independent variables and the coefficients from equation 14 of table

4^14, the calculated contributions to the percentage

Table 4-15. Calculated contributions of independent variables to 84-day sulfate expansion of cements having 8 to 15

percent C3A

Independent

variable

Values used

for independent

variable

Coefficients from

equation 14, table 4-14

Calculated

contribution

to SEsi

Calculated range of contribution to SE84

Const. = +0.0330

(C3A)3_ 512 -3375 -1-0. 00017 +0. 087 to +0. 574 0.487 Ca0/Si02 2. 4- 3.

3

-0. 125 -0. 300 to -0. 413 0.113 Cr.__ 0- 0.02 -f-3.37 0 to +0. 066 0.066 v 0- 0.1 -0.78 0 to -0. 078 0.078 P 0- 0.5 -0.25 0 to -0. 126 0.125

Table 4-16. Range and variance of duplicate tests as compared to the S.D. values obtained for equations at I4, 28, and 84 days

Col. 1 Col. 2 Col. 3 Col. 4 Col. 5

Age of expansion measurement

Range of percentage expansion of

21 cements

(Variance) "2

of duplicate

tests

S.D. values

of equations

for NAE

cements,

table 4-17

Ratio of variances (squared values

of column 4 divided by

squared values

of column 3)

Days

14_ Percent0. 014-0. 056

0. 016-0. 083

0. 025-0. 185

0.0025

0.0028

0.0036

0.00443 0.00649

0. 01168

3.2

5.3

10.6 28

84

expansion at 84 days of the prisms are presented in

table 4—15. Also presented in this table are the

calculated ranges of the computed values.

6.8. Tests on a Supplementary Series of

Cements

The 21 cements used in the supplementary tests to evaluate the reproducibility of the test method

had expansion values within the range obtained

for the type II, IV, and V cements in the studies

reported in this article. The variance of duplicates calculated from these 21 cements was therefore compared to the (S.D.)^ values obtained for

the equations with the lowest S.D. values computed for the cements having 0 to 9 percent C3A.

The results of these comparisons are presented in

table 4—16. The variances of the duplicate tests at each of the ages indicated were significantly lower

than attained in the equations as judged by the

ratio of variances as presented in the last column.

6.9. Autoclave Expansion and Sulfate Expansion

Information was not available on the glass content or rate of cooling of the clinker used in the

manufacture of these cements. It has previously

been reported that rapidly quenched clinker having high C3A content has greater sulfate resistance

than slowly cooled clinkers although this is not

the case with the C4AF constituent [2, 3]. It is also known that rapid quenching of high magnesia

16
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cements results in lower autoclave expansion. It

is generally recognized then that the results of the

autoclave expansion test are affected by (among

other things) the rate of quenching of the cement

clinker during manufacture. Attempts were therefore made to use this property to further reduce

the S.D. values.

Equations were computed for both the cements

containing 0 to 9 percent C3

A and those containing 7 to 15 percent C3A including as an additional in- dependent variable the autoclave expansion, ratios

of autoclave expansion to MgO and/or C3A contents, or the reciprocals of these values or the products of the MgO and/of C3A values times the autoclave expansion values. The use of the products

of the MgO and the C3A times the autoclave ex- pansion as additional independent variables in the

equations resulted in significantly lower S.D.

values only with the cements having 0 to 9 percent

C3A whereas this was not the case for cements having 7 to 15 percent C3A. The equations 1, 4, 2, 5, 3, and 6 presented in table 4—17 for cements containing 0 to 9 percent C3A may be compared with equations 5 and 12 of table 4—4, equations 6 and 19 of

table 4^6, and equations 8 and 19 of table 4—8, re- spectively, in which other independent variables were the same. It may be noted in table 4r-17 that

SrO hasa coefficient/s.d. ratio of less than 1 in five of the six equations, which was not the case in the

previously reported comparable equations. It may

also be noted that the sign of the coefficient for

MgO

X autoclave expansion was minus while that

for the C3A

X autoclave expansion was plus. No

satisfactory explanation can be offered for this

apparent anomaly.

7. Discussion

In plotting the expansion values of the mortar

prisms made of different cements versus the age

of the measurement, it was noted that smooth lines could be drawn with only slight deviations of the

plotted points from the lines. With cements having low expansion values, the rate of expansion at the later ages was not so great as at the earlier ages, i.e., 0 to 14 days or 14 to 28 days. Cements

having high expansion values at the early ages

had, in many instances, more rapid rates of expansion at the later ages. This occurred between 2

and 3 months with some cements. In some in- stances the specimens warped in the 4- to 6-month

period, making the measurements after that condition had occurred of questionable value. Up to the age of 84 days the plots of expansion versus age indicated only few instances where the plotted

lines of the different cements crossed one another. A greater difference between expansion values for

different cements was obtained at 28 days than at 14 days, which could result in a better discrimination between the cements. The more rapid expansion after two months did not occur uniformly

with all of the cements of high potential C3A content.

18
Plotting the 14-, 28-, and 84-day sulfate ejjpansion values of the different cements versus the vari- ous independent variables indicated that in general the same variables had a significant effect at the different ages. The individual plots shown in figure 4-1 indi- cate no apparent relationship between the MgO

contents of the cements and the expansion values.

MgO also did not turn out to be a significant variable in equations relating the expansion at vari- ous ages to various independent variables. These

expansion values were obtained at a relatively

early age and it may be possible that the suspected

effect of MgO is masked at the early ages and

could become more apparent at the later ages. Some exploratory computations of the relationship

of the expansion values at six months of the ce- ments having 0 to 9 percent C3A and the MgO

content indicated no significant contribution of

the MgO to the expansion. The MgO contents of

the cements used in this study were all below 5.0 percent and it has previously been reported [2]

that deleterious effects are obtained only with

higher MgO contents.

It was noted in figure 4-1 that there was no apparent relationship between the potential C3S content of the cement and the expansion of the mortar

prisms of the different cements whereas there ap- peared to be some relationship to the potential

C2S content. In the computed equations there was

evidence that high values of CsS were associated

with low expansion values or that FeaOs and the

CaO/Si02 ratio wei'e associated with the expansion values. The fact that high C3S content of

cements is usually associated with high early

strength prompted calculations of equations re- lating the compressive strength of 2-inch motar

cubes made from the cements to the sulfate expansion values obtained with the motar prisms.

Equations were computed for the relationship

between the sulfate expansion values at 14, 28,

and 84 days and the compressive strength at 1, 3, 7, and 28 days, and 1 year, of 2-inch mortar cubes

made of 1: 2.75 (cement to graded Ottawa sand)

mortar stored in water after the original 24-hour

moist curing. Also computed were equations with

the strengths at the different ages and including

(CsA)^ for the 14- and 28-day sulfate expansion

and (CaA)^ for the 84-day expansion. These computations were all made without separating the

cements into the two groups of high and low C3A

content. The equations for the AE-hNAE and

for the NAE cements are presented in table 4^18.

The "F" values presented in the last column in

this table show that when strength alone was used

as the independent variable (equations 1 through

15 and 31 through 45) there was no relationship

between the sulfate expansion and the compressive

strength at 1, 3, 7, or 28 days but there was a significant relationship between the expansion at each of the 3 ages and the 1-year compressive

strength. However the multivariable relationships using (CaA)^ or (CgA)^ together with the

compressive strengths at the various ages (equations 16 through 30 and 46 through 60) present

evidence to the effect that the compressive strength

at the early ages (1, 3, and 7 days) may be asso- ciated with a reduction in the .sulfate expansion

values. (The "F" values for these equations were

in each case over 200 primarily because of the in- clusion of the C3A as one of the independent

variables.)

The coefficient/s.d. ratio for 1-, 3-, and 7-day

strength ranged from about 1.0 to 2.0 for the different combinations which does not indicate a highly significant effect. In these equations (16

through 30 and 46 through 60) the coefficients for

compressive strength were highest with the 1-day

strength and were successively lower when the

strength at later ages was used as an independent

variable. The sign of the coefficients was in each

instance minus and in this respect consistent with

the effect that high C3S cements (normally asso- ciated with high early strength) also were asso- ciated with low expansion of the mortar prisms.

Both Federal and ASTM specifications at one

time limited the amount of potential C3S permitted in the Type V sulfate resisting cements, but

this limitation was later removed. The proposed

test [5] which is of short duration indicates that

a high C3S content is desirable. Miller et al. [1],

quoted a number of references (No. 90, 98, 100,

351, 354, 357, 361, and 398 for example) which in- dicated that cements with high lime content or C3S are more susceptible to certain types of sulfate

attack than cements with low C3S content. Lea

and Desch [3, page 299] , have indicated that C3S

expands rapidly in magnesium sulfate solution

and very slowly in sodium or calcium sulfate so- lution. The use of calcium sulfate as in the pres- ent study and in the proposed ASTM test for

potential sulfate expansion [5] may, therefore,

not properly evaluate the resistance of portland

cements where magnesium sulfate as present in sea water contributes to the deleterious reactions. On

the other hand, it appears well established that

high-quality concretes made with sufficient cement

and low water-cement ratio as well as adequate

curing or autoclaving prior to exposure to sulfate

solutions have superior sulfate resistance. Other

factors being equal, high C3S cements tend to form

their hydration products more rapidly and would

require less curing time to attain the degree of

hydration and impermeability necessary for re- sistance to attack by sulfate solutions.

There is a great deal of evidence in the literature

to the effect that the use in concrete of finely

ground silica and other pozzolanic materials tends,

as a general rule, to improve the resistance to sul- fate attack. This improved resistance has been

attributed to the reaction of the pozzolans with

calcium hydroxide, a product of the hydration of

C3S, but may also result from the enhanced impermeability of the concrete.

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22
Portland-blast-furnace-slag cements have, ac- cording to many references, a good record with

respect to sulfate resistance in service. Cements

of this class, having somiiwhat lower strengths at early ages, tend to have high expansion values

when tested by the methods used in this study.

For example, using the same test procedures as for the Portland cements, tests were also made on

seven commercial portland-blast-furnace-slag ce- ments. The average 14-day expansion was 0.093

percent. All of these cements had 14-day expansion values greater than the 0.045 percent limit

which has been proposed and one of the cements

had a 14-day expansion value of 0.133 percent.

In determining the variables associated with the

expansion at the various ages of the prisms made

of the dilferent cements, a large number of equations were computed. The equations presented in

this section were selected because of their relevancy

to the problem. Advantage was taken of supplementary statistical tests previously described [10] to determine which of the available independent

variables were possible contributors to the deviations between observed and calculated values.

The final criterion was the behavior of these variables in the multiple regression equations. It seems unlikely therefore that any independent

variable not used in the respective equations could

have a major effect on the relationship presented.

In the computations of the multivariable rela- tionships the potential C3A or some power of the

C3A was usually used as one of the independent

variables in each of the series of equations. However, it was also demonstrated that the AI2O3 content of the cement could be used as an independent

variable providing other significant variables were

also employed, and this resulted in equally good

agreement between the observed and calculated

expansion. Similarly the potential C3S was used

in some instances, whereas the CaO/SiOa ratio was

used in most of the equations. With a given FegOs

content the amount of C3S as calculated would in- crease with the increase in the CaO/Si02 ratio. The FeaOs was used rather than the C4AF because

of the fact that the C4AF is computed as a constant

times the FeaOs content for the range of FcaOs

present in these cements. For the cements having 0 to 9 percent C3A, ex- pansion increased with increasing Fe203, loss on

ignition, and K2O of the commonly determined

variables (in addition to C3A), while it decreased

with increasing CaO/SiOa and insoluble residue.

The effect of these commonly determined variables

other than C3A appeared to decrease with age at which measurements were made, i.e., the coefficients were closer to zero at the later ages. Other independent variables such as SrO, Cu, V, Zn, and Ni

also appeared to be associated with the expansion

of these cements. Of these trace elements, Cu was

the only element associated with low expansion

values. V and Zn appeared to be associated with

high expansion values at 14 days (although coefficient/s.d. for Zn is not significantly large),

whereas Ni appeared a.ssociated witli the expansion

values at the later ages. The coefficient/s.d. ratif>s of the individual trace elements were not highly

significant but it appears that further studies by

other means are warranted. Tlie limitations of

the analyses by methods employed in this section

have been discussed in a previous section [10].

Wliereas plots and computations of the multivariable relationships indicated that the use of

linear relationships appeared adequate for cements

having 0 to 9 percent C3A, this was not true for the

group of cements having 7 to 15 percent C3A,

where lower S.D. values were obtained when using

the second or third power of the C3A contents of

the cements. For cements having 7 to 15 percent

C3A the coefficient for Fe203 was negative, with a high coefficient/s.d. ratio at all three ages, whenever C3A was not included as a variable, indicating

that expansion decreased with increasing FejOs

content. When C3A was used as a variable instead

of AI2O3, however, the coefficient of Fe203 was not

significant in most cases. This apparent anomaly

results from the method used in computing the potential compound composition [8] in which the

Fe203 is assumed to require an amount of AI2O3

sufficient to form the C4AF in those cements having a high AI2O3 content. With this group of cements and the variables

used, high values of CaO/SiOj were associated

with low expansion values. Whereas the loss on

ignition may be significant at 14 days, the coeffi- cient/s.d. ratio was less than one at the later ages. The insoluble residue and K2O contents were apparently not associated with the expansion of

these cements as with the cements of low C3A content. Of the minor constituents and trace ele- ments, SrO appeared significant at 14 days but not

at later ages. P appeared significant at the later ages, although statements about this element are doubtful because of the few cements which had a measurable amount. Cr and V also appeared to be associated with the expansion values. Cr203

and P2O5 are both included with the AI2O3 in the

usual chemical analyses of portland cements unless

the AI2O3 is corrected for these oxides. Unless

such corrections are made, their presence will detract from the accuracy of the calculated potential

C3A content. It is of interest to note, however,

that in the computations in this article the sign

of the coefficient for P is minus and for Cr it is plus. Hence it would appear that their presence

in the equation is not primarily as a correction for

the lack of accuracy of the AI2O3 and/or the C3A

content. Although the Cr values reported appeared to present a reasonable distribution of

values in the different cements, P which is believed

present in minor quantities in most portland ce- ments was reported only for those cements having

0.1 percent or more P as determined by the spec- trochemical method. More refined procedures

than those employed in the present study will be

208-577 O—6& 4 23
required to verify the effect of the trace elements on the sulfate expansion as measured by the potential sulfate expansion test or in determining the

effect, if any, on the susceptibility to sulfate attack

of concretes containing varying amounts of these

elements.

In comparing the equations computed for the

AE + NAE cements with those computed for the

NAE cements only slight differences were noted

in the magnitude of the coefficients or the coeifi- cient/s.d. ratios. However, there were only 5 air- entraining cements in the 0 to 9 percent C3A group

and 11 air-entraining cements in the 7 to 15 percent

C3A group on which the computations were made.

Because of the relatively few air-entraining ce- ments in each of the groups, it was of no value to compute multivariable regression equations for

these cements by themselves.

Computations were made comparing the observed values for expansion of the mortar prisms

of the cements common to both the 0 to 9 and 7 to 15 percent C3A versus the values computed by the

equations for the respective groups. These studies

indicated that the computed expansion values for

cements having 7 to 9 percent C3A were more in

accord with the observed values when using the

equations developed for the group of cements having 0 to 9 percent C3A.

It was pointed out in part 1, section 1 of this

series of articles that limitations of the ranges of

certain variables made the task of evaluating the

true effect of such variables more difficult. If,

however, a group of cements used in an equation

includes one with very unusual properties, this one cement may affect not only the ratios of coefficients to s.d. values of the other variables, but also the

S.D. value of the equation. An example of such an effect is presented in table 4-19. Five pairs of

equations were computed for cements containing

7 to 15 percent C3A with and without a cement

which, as previously noted, had a high autoclave

expansion. It may be noted that the coefficient/

s.d. ratios with this cement excluded were less than

one in many instances where the coefficients with it were of marginal significance. The S.D. values

of equations without this cement were lower than

in corresponding equations where it was included.

All of the cements other than the one cited above

had low autoclave expansion values which indicated that the free calcum oxide contents were very

low. Because of this and the questionable signifi- cance of very small values of free calcium oxide as determined by available methods, no analyses were made of this constituent. This variable may have

been one of the many unknown factors contributing to the lack of better agreement between the

computed and determined expansion values.

8. Summary and Conclusions

Studies were made of the relationship of cement

composition to the expansion of mortar bars in the

test for potential sulfate resistance of portland

cements. In this test sufficient molding plaster was

added to the cement to make the SO3 content 7.0 percent. Measurements were made at 14, 28, and

84 days of the expansion of 1 : 2.75 (cement plus

CaS04 to graded Ottawa sand) mortar bars made

of 183 Portland cements of different types having

a normal range of chemical compositions.

Plots of the expansions of the mortar bars ver- sus age after fabrication indicated that up to 2 or 3 months there were few cements which changed

their relative rating in the group of cements. Somewhat greater differences in the expansion

values were obtained at 28 days than at 14 days

which afforded a better discrimination between

the cements. At later ages the prisms made from some of the cements of medium or high C3A content warped or deteriorated, making measure- ments after three months of questionable value.

Plots of the expansion values of the prisms made

of the different cements versus the C3A content of

the cements indicated a general relationship. Plots

of the expansion values of the different cements

versus other variables indicated to some extent the

independent variables associated with the cements

having high or low expansion values.

Multivariable relationships were computed by

a least squares method of the relationship of the

expansion values of the mortar bars at the differ- ent ages and various combinations of independent

variables. The computations of the equations were made on cements having 0 to 9 percent potential

C3A and on cements having 7 to 15 percent potential C3A. Whereas a linear relationship appeared

adequate for the low C3A cements, the use of the

second or third power of the C3A in the high C3A

cements resulted in better agreement between the

observed expansion /alues and those computed by

the equations. In addition to the potential C3A

content of the cement, other commonly determined

variables associated with high expansion values for

the low C3A cements were as follows : high values

for the FcaOs, loss on ignition, and K2O; and low

values of the CaO/Si02 ratio and insoluble residue.

The effect of these variables decreased with the

increase in the age at which the expansion meas- urements were made. Other independent variables such as SrO, Cu, V, Zn, and Ni were also as- sociated with the expansion of the prisms. Cu

was the only one of these trace elements for which

high values were associated with low expansion

values of the prisms. The calulated contribution

of the trace elements to the expansion values in- creased with the age at which expansion measure- ments were made.

For cements having high C3A values, high

values for FeaOs and CaO/Si02 were associated

with the cements having low expansion values for

24
CO

CO »o ^

O O O O

(M CO o o o o

O i-H !M i-H r-4 .-I (M i-H OO OO OO OO OO OC OO OO OO OO OO oc o o OO

I ^

o o o o o o OO

88

0*0

S?3 o o 00

lO-* 1-1 (N CD iM OSi-i i-t Oi »0 f IOCS CD O Tt" C3i CDO CDOO OC (MO o T-H c<i o o r-i oao .-H c 00 00 00 00 00 o< 00 00 00 00 00 00

t- -H CD TjH to CO iM 2; rH Tft rH CIO iM cot- <MTt< aO(M So 00 00 So So 00

^9OloQ 00

Tt* CD CO r-- r-- oot- cot^ tor-- c^un

CD iM 03 CSJ 03 CM CM 00(M cD IM 00 00 00 00 00 00 00 00 00 00 00 00 00 00

00 00 00 00 00 o o o o

o c» o 00 00 00

CD OS -^(M

01

0

O O

r^ OS 05 Oi o o 00

o o o o 00 o o

a> o oo o

o* o +^

OS o 00o o

CC 01 tD CO 00 OS o 00 00

O CO

CD CD

CM O CM O 00 00 00

« o CO r-- M CO 00 1-1 03 OS

<n OS

CO d

00 CD ro 00 00 0000 CO

t- o CD CO

1-1 Ct> ^ ^ O W W OS

CO CO CO 00 00

00 00 00 1^ Io o 00 o o 00 00

+

<1

tH ^ N

Table 4-20. values for significance of reduction of variance due to added variables

Critical

F" ratio Table Equations "F" ratio D.F.

0=0.01 a=0.06

1.

4

16. 2 5:97 3. 22 2.32 4,5 3.7 4:93 3. 53 2. 45 4-4 6,7 3. 9 4:93 3. 63 2. 46

8,11 16.3 6:92 3.22 2.32

11, 12 3.8 4:88 3. 52 2. 48 13,14 3.7 4:88 3. 54 2. 48

1,4 11. 8 5:97 3. 22 2. 32

4,6 4.2 3:94 4. 00 2. 71 4-6 10,12 4.3 3:94 4. 00 2. 71

14, 17 11.7 5:92 3. 22 2.32

17, 19 4.

1

3:89 4. 02 2. 72

23, 26 4.

1

3:89 4. 02 2. 72

1,6 7.0 5:97 3. 22 2.32

2,7 8.6 5:97 3.22 2.32

4-8 6,8 6.6 3:94 4.00 2. 21 7,9 4.7 3:94 4. 00 2. 21 12,17 6.4 5:92 3. 22 2. 31 17,19 5.6 3:89 4.02 2. 71

1 3 5.

1

3:108 3 97 2. 69

1.4 4.2 5:106 3. 18 2.30

4-10 5,6 2.7 3:105 3. 98 2.70

7,9 4.6 3:97 4. 00 2. 70

7, 10 4. 2 5:95 3. 22 2. 31 11,12 2. 5 3:94 4. 00 2. 71

1,3 3.9 1:110 6. 87 3. 93 3,4 11. 3 3:107 3.97 2. 70

10, 11 16 7 2:109 4. 83 3.08

4-12 11, 12 11.1 3:106 3.98 2.70

14, 16 2. 7 1:99 6.90 3. 93

16, 17 10. 0 3:96 4. 00 2. 71 23,24 14.8 2:98 4. 83 3.08

24, 25 9. 9 3:95 4. 00 2. 71

1, 3 5.0 1:110 6. 87 3.93 3,4 9.2 3:107 3. 97 2. 70 8,9 21.0 2:109 4. 81 3.08 4-14 9, 10 6.

6

3:106 3. 98 2. 70

11, 13 4.6 1:99 6. 90 3.99

13, 14 10.2 3:96 4. 00 2. 71

18, 19 19.6 2:98 4.83 3.08

19, 20 5.8 3:96 4. 00 2. 71

the prisms at all ages. Of the minor or trace ele- ments, SrO, Cr, V, and P appeared to be associated

with the expansion values, the SrO at 14 days, and

the P at later ages. The calculated contribution of

the trace elements (other than SrO) increased

with the age at which the expansion measurements

were made.

The observed and computed values of the ex- pansions of cements having 7 to 9 percent C3A

were in better agreement when the equations computed for 0 to 9 percent C3A cements were used

when the equations for the 7 to 15 percent C3A

cements were used.

The use of the products of the autoclave-expansion values and MgO and C3A contents of the

cements, respectively, as additional independent

variables in the equations resulted in lower S.D.

values for the low C3A cements but not for cements

having high C3A contents. The difference between determined values and

those computed from the equations as indicated by

the standard deviation values of the best equations were larger than the standard deviation values of

duplicate determinations made on a different

group of cements in a supplementaiy series of

tests, but no more than would be expected in view

25
of the larger error that would be found with a

large number of tests spread over a comparatively

large period of time as compared to that obtained

from duplicate tests run close together. However,

a need is still indicated for further study to determine the additional variables which may be in- volved in the test for potential sulfate expansion of cements. Regression lines computed to determine the re- lationship of the expansion values of the cements

to the compressive strengths of the 1 : 2.75 (cement

to standard Ottawa sand) mortar cubes indicated

that the expansion values obtained were not asso- ciated with the compressive strength alone at the

early ages but were related to the compressive

strength at one year. However, if a function of

the C3A was included as an independent variable, a relationship between the strength of the mortars

and the expansion appeared, the cements with high

compressive strength values being associated with

those cements havmg low expansion values.

In conclusion it would appear that, in view of

the highly significant relationships existing not

only for the potential C3A content, but for other

commonly determined variables together with the

relationship of certain trace elements to the sul- fate expansion values obtained in the test for potential sulfate resistance of portland cements,

further studies are warranted and desirable to determine the possible effect of such variables on

the susceptibility of concretes exposed to sulfate

attack.

In addition to the acknowledgements indicated

in previous sections in 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 expansion values at various ages.

9. References

[1] Dalton G. Miller, P. W. Manson, and R. T. H. Chen,

Bibliography on sulfate resistance of portland

cements, concretes and mortars (Annotated), University of Minnesota Paper No. 708, Miscellaneous

Journal Series (1952).

[2] R. H. Bogue, The Chemistry of Portland Cement,

2d Ed. (Reinhold Publishing Corp., 1955).

[3] F. M. Lea and C. H. Desch, The Chemistry of Cement

and Concrete, Revised Edition (Edward Arnold

Publishers Ltd., London, 1956).

[4] Proceedings of the Third International Symposium

on the Chemistry of Cement, London 1952, Cement

and Concrete Association, 52 Grosvenor Gardens,

London, SW 1. [5] Report of Working Committee on Sulfate Resistance

of ASTM Comm. C-1 on Cement, A performance

test for the iKttential sulfate resistance of portland

cement, Bui. ASTM, Feb. 1956, p. 37. [6] P. H. Bates, Portland cement theories (Proven and

Otherwise) and si)ecifieations, ASTM Proc. 40,

pp. 469-500 (1940).

[7] F. R. McMillan, T. E. Stanton, I. L. Tyler, and W. C.

Hansen, Long time study of cement performance

in concrete. Chapter 5—-Concerte exposed to sul- fate soils. Research Laboratories of the Portland

Cement Association, Bui. 30. [8] Federal Specification : Cements, Portland. SS-C192 (1946) and SS-C-192(d) (1960).

[9] Standard Specifications for Portland Cement, ASTM

Designation C150-^2 (as revised to 1968).

[10] NBS Building Science Series No. 2, Interrelations Between Cement and Concrete Properties, part 1, section 1. Materials and techniques.

[11] NBS Building Science Series No. 2, Interrelations Between Cement and Concrete Properties, part 1, section 2. Water Requirements of Portland Ce- ments.

[12] NBS Building Science Series No. 2, Interrelations Between Portland Cement and Concrete Properties, part 1, section 3. Occurrence of Minor and

Trace Elements in Portland Cements.

[13] R. G. Shelton, Action of Sodium and Magnesium Sul- fates on Portland Cement, J. Ind. and Eng. Chem.

18, 854 (1926).

26
Section 5. Heat of Hydration of

Portland Cements

R. L. Blaine and H. T. Arni

The relationships between the chemical characteristics of portland cements and the heat of hydration at 7 and 28 days and at 1 year were studied by computing multivariable

regression equations with the aid of a digital computer and determining which of the independent variables appeared to have a slgniflcant relationship to the heat of hydration

values. The computed equations verified to a reasonable degree effects usually attributed

to the major potential compounds. Other commonly determined variables, such as fineness and loss on ignition, were associated with the heat of hydration at all ages ; K2O and SO3

with the 7 day ; and NazO with the 1-year heat of hydration. Of the other minor constitu- ents Cu and P appeared to be associated with the heat of hydration at all ages. In addition,

Or and Zr were associated with heat of hydration at 7 days ; Co, Zr, and SrO at 28 days

;

and V and Ba at 1 year.

Contents

Page

1. Introduction 27

2. Materials and test methods 28

3. Statistical analyses 28

4. Results of tests . 28

4.1. Plots of heat of hydration versus independent

variables 28

4.2. Heat of hydration at 7 days 29

4.3. Heat of hydration at 28 days 31

4.4. Heat of hydration at 1 year 33

5. Discussion 35

5.1. Age of test versus trace element effect- 35

5.2. Effect of minor constituents and trace elements on calculated coefficients of the major calculated compounds 35

5.3. Numerical values of coefficients of the major

potential compounds at different ages of test- 36

5.4. Comparison of coefficients of major potential

compounds obtained in this investigation

with previously reported values 36

5.5. Heat of hydration and compressive strength. 38

6. Summary and conclusions 38

7. References 40

1. Introduction

The heat of hydration of portland cements has

been dealt with rather extensively in books by

Lea and Desch [1] ^, Bogue [2], and Taylor [3] as well as by different authors in the "Proceedings" of the London [4] and Washington [5] symposia on the chemistry of cement. The values re- ported by Lerch and Bogue [6] as well as Thorvaldson, Brown, and Peaker [7] on compounds

hydrated independently ; and the values obtained

by least squares analyses and reported by Woods,

Steinour, and Starke [8] ; Davis, Carlson, Troxell,

and Kelly [9] ; and Verbeck and Foster [10] have

also been widely quoted. Generally, the heat of

hydration determined by the heat of solution

method has been evaluated statistically in relation

to the potential compounds or major oxides present

in portland cement. However, studies have also

been made of its relationship to other factors such

1 Figures In brackets indicate the literature references at the end of this section.

as fineness and rate of cooling of clinker [11],

water-cement ratio [12], and curing temperature

and loss on ignition [13], all of which may have

an appreciable effect on the heat of solution values.

Schwiete and Tan Tik-Ien [14] have demonstrated

that other oxides such as MgO and AI2O3 incorporated in the tricalcium silicate phase have an

effect on the heat of solution values. Other ele- ments are also known to act as "stabilizers*' for some of the potential compounds and are believed

to affect the hydration process. Although Copeland and Kantro [15] and Verbeck [16] have

summarized studies by many investigators on the

heat of hydration of cements, no comprehensive

literature is available on the effect of minor constituents. This section of the series on the Interrelations Between Cement and Concrete Properties

deals, therefore, not only with the effects of potential compound composition and major oxides on

the heat of hydration, but also with the effect of

the minor and trace elements.

27
2. Materials and Test Methods

The Portland cements used in this series of tests have been described in sections, 1 and 3 of part 1, dealing with Materials and Techniques [17] and

Occurrence of Minor and Trace Elements [18].

As indicated in these previous sections, the cements were procured from different areas of the United

States with only a few from other countries. The

different cements were classified into different

types, primarily on the basis of their chemical

composition. The heat of hydration values were

not taken into consideration at the time the cements were so classified. The heat of hydration values were determined

at 7 and 28 days and 1 year by the heat of solution

method described in Federal [19] and ASTM [20]

specifications. The 7- and 28-day tests were made

on most but not all of the portland cements whereas

the 1-year tests were made on slightly moi*e than

half the cements. Duplicate tests were made on

most of the cements tested. All tests were con- ducted at the Seattle laboratory of the National

Bureau of Standards under the supervision of

F. N. Winblade and G. Watton.

The notations HH(7), HH(28), and HH(IY)

are used in this section to designate the heat of hydration at 7 days, 28 days, and 1 year respectively.

Other commonly used notations and abbreviations

have been presented in section 1 [17].^

3. Statistical Analyses

The statistical tecliniques used to determine the

independent variables associated with the heat of

hydration values have been described in a previous

section of this series on Materials and Techniques

[17]. These techniques included plots of the dependent and major independent variables as well

as the use of the "tic-tac-toe" and the Student's

"t" test of the "hi-lo" and "middle ends" variations to determine which of the minor constituents or trace elements were probable contributing fac- tors to variations. The equations obtained by tbe

least squares method (tables 5-2, 5-3, 5-6, 5-7,

5-10, 5-11, and 5-14) were the most important means of drawing conclusions. As in previous

sections, comparisons were made of the degree of

fit using only major constituents, these with com- monly detemined variables and these together

with the minor or trace elements. Equations were

also computed for the "odds" and "evens" in the

array of cements. Abbreviations employed in pre- vious sections are also used in this section.^ In

addition "F" values for the reduction in variance

due to added variables in a number of pairs of

equations are given in table 5-13.

In calculations of the least squares equations

three white cements and a cement with high auto- clave expansion were eliminated from consideration. Certain other cements reported had heat of

solution values which consistently showed excessively large deviations in preliminary equations,

and these were also eliminated in the final equations. No reason was apparent for their non- conformance.

Most authors indicated by previous references

[1 through 10] have assumed that the heats of hydration of the potential compounds in portland

cement are additive and that relationships between

heat of hydration and constituents are essentially

linear and pass through the origin. In this study some equations were computed both with and

without a constant term. The constants, when cal- culated, did not differ statistically from zero (i.e., the s.d. of the constant was large in relation to the constant) and the assumption of a zero constant appeared to be most consistent with known

facts regarding the hydration of cement compounds. Therefore, no constants are used in the

equations presented in this section.

4. Results of Tests

4.1. Plots of Heat of Hydration Versus Independent Variables

In figure 5-1 are presented the results of plotting

the heat of hydration values at the three ages ver- sus various independent variables. The procedure

for dividing the values into 12 groups, plotting of

the points, separating into quadrants and evaluating the relationship on the basis of the number

and position of the points in the four quadrants

2 The notations C3A, CsS, C2S, and C4AP are used as is cus- tomary in cement technology for the potential trlcalcium aluminate, tricalcium silicate, dicalcium silicate, and tetracalcium

aluminoferrite, respectively. The terms A/F and S/(A-|-F) re- fer to the ratios of AI2O3, Fe203, and SiOo. Also used are Loss

for loss on ignition and APF for air-permeability fineness. AE is used to designate the air-entraining cements and NAE for the non-air-entraining cements.

has previously been discussed (see sec. 1 [1^])-

As previously indicated [17] an absolute value of

11 or greater in the line "note 4" can be considered

significant at the 95 percent level. It may be noted

that Si02, AI2O3, Fe203, and SO3 met this requirement at each of the three ages. K2O and total

^ Among the statistical terms used in this and other sections

of this series are the following : S.D. = Standard deviation calculated from the residuals of a fitted equation, or the standard deviation about the average.

s.d. =Estimated standard deviation of the coefficient of an

individual independent variable when used in a fitted equation.

Coef./s.d. or Coefficient/s.d. = Ratio of the estimated coeffi- cient (of an independent variable used in an equation) to

its estimated standard deviation.

"ii"' =Fisher's ratio of variance estimates. Critical "F"

values were obtained from tables presented in most text- books on statistics.

28
HEAT OF

HYDRATION INDEPENDENT VARIABLES

AGE NOTE Si02 AlaOj FegOj CqO MgO SO 3 NazO KgO

TOTAL

Alkali C3S C4AF A

F

S A +F

Air p. Fine. Wagn.

Fine

7 DAY

(1)

(2)

102 IV120

120 |\|\102

j /

6

6

102 7

3

102102

120

1 /\/

102120

1 \

120 |\

1 \

120 \/

102102 V6

6

(3)

(4) NL

-18

L + 24

L -24L? + 12 NO

+ 3 L + 15 NO+ 2

L + 17 L + 15 L + 24

L + 12 L -24

L -24L + 24 NL

-14 NL + 10 NO + 1

28 DAY

(1

)

(2)

120120

1 /

120

102

1Y

_6_6

120 \/

8484

1 /

V

_6_6

120

1 / v

iO

2

1 /

\/

_!20 |\

1 \

120

1 \

_!2_ 0v

102 IV102 Y

_6.6

(3)

(4) NL -24

L + 24L -24

NL + 9 NO

0

L +24NO -4L? + 8 NO + 5

L + 24

L +17L -24L -24

L + 24 NL

-14 NL + 17 NO + 1

1 YEAR

/ 1 ^ 102 |\

1 \

120120

1 \

84

\/

6

6

102

1 /

6

6

84

/

84

1 / /

\/

120

102 V

102 |\102 |\1 \120

\/

10284

\/

8

4

(3)

(4) L -19

L + 24L -18L + 11 NO + 1 L + 17 NO -4

L? + 8 L? + 1 L + 24L + 17 L -18

L -17L + 24 NO

-17

L?+6

NO

0

FiGXJBES &-1. Results of plotting heat of hydration at 7 days, 28 days, and 1 year on the "y" axis versus various

independent variables on the "x" axis. Note 1, ratio of plotted points occurring In pairs of diametrically opposite quadrants. Note 2, general trend of line drawn through the plotted points. Note 3, apparent nature of the relationship, —L=linear, NL= non-linear, NO =no apparent relationship, and N? =not

determinable. Note 4, quadrant sum (see Part 1, section 1 of this series of papers).

alkali bad a quadrant sum greater than 11 only

for the 7 day tests, whereas NajO showed no

significant relationship at any of the a^es at which

the tests were made. The relationships of C3A,

C3S, C2S, and C4AF to heat of hydration were

highly significant at all ages, but the slopes of

both C2S and C4AF were negative. This probably

results from the predominant effect of C3A and

C3S. As the Fe203 increases, the C4AF increases

and the C3A decreases. Also, as the amount of

C3S in Portland cement increases, the amount of

C2S generally decreases. The A/F and S/ ( A+ F

)

ratios have highly significant relationships to the

heat of hydration values with the latter having a negative slope. The effect of fineness, especially

as detemtiined by the turbidimeter method, was

apparently masked by the other more important

variables.

4.2. Heat of Hydration at 7 Days

The frequency distributions of the 7-day heat

of hydration values of the cements of the different

types are presented in table 5-1. Each of the types

of cement (classified on the basis of chemical composition) had a considerably broad distribution of

values and there was an overlapping of the values

obtained for the different types of cement. Five

of the 16 cements originally classified as type I cements, but later classified as type II when the

maximum of 50 percent for C3S was deleted, had

heat of hydration values greater than the 70 cal/g

permitted by specifications for type II cements. In table 5-2 are presented selected equations

computed by the least squares method for both the

Table 5-1. Frequency distribution of cements with respect

to heat of hydration at 7 days

Heat of hydration, calories per gram

Type 40 45 50 55 60 65 70 75 80 85 90 95 Total cement to to to to to to to to to to to to

46 50 55 60 65 70 75 80 85 90 95 100

Number of cements

I 1 2 113

5

1 13

19

13

19

12

16

2 10 2 80

7

16

1 48

1 19

115

188

lA.. _ 11* 6 IIA*

II 1 8 21

1 6 IIA..

Ill 1 3 2 6 4 2

1

1 IIIA rv and V

Total

1

1 23

2

2 615 434 34 31 24 24 14 5 1

'Originally classified as type I or lA. AE + NAE and the NAE cements. Use of only

the major potential compounds as in eqs 1 and 4

resulted in highly significant reductions in the

S.D. values. ( See table 5-13. ) The added effects of other commonly determined variables, K2O,

SO3, loss and fineness, each of which appeared to have a significant relationship to the heat of hydration, are presented in eqs 2 and 5. The coef./s.d.

ratio for C4AF was less than one when the additional variables were included, with both the AE +

NAE and the NAE cements. The additional use of the trace elements, Cu, Cr, Zr, and P as in eqs 3

and 6 resulted in further significant reductions in the S.D. values and in a reduction of the coef./s.d.

ratio for C2S to less than one. (See table 5-13.)

The change of the coefficient or of the coef./s.d.

ratio for a compound when added variables are

29
CO c + +

o

OS

CD

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00 M CO O 05 O CP •or- 00 o + +^ CO ^

CO O CO

eo »o

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CD O MO

O CO .-H oo oo oo oo

CD ^ o oo

o o oo o o

oco

OS i-H ^ rH CO <N Oi

CO o O CO

l>-CO

t- N ^ eo~

l>- CO OS

OS OS

00 CO

CO 1-1 CO f-H rCD y-* 3S 5So »o to i-H 00 w CO

o OS

(N o

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1 ^ OS1 ^ 1 ^

+

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1-H l-H T-l

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CO OS

CO tfi 00 t- O ^ 00 O CO oo o o o o oo oo oo o o oo oo oo

"4-1

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d GO +

»0 OS

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C4 rH

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S o oo oo oo

Tt< S S rH SrH eo rH o o o oo oo

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OS »0 « CN ^ -n* 00 O 00 00 kO

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» rH oo OSCO CprH ^ CM O ^t^ »OQ O

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to o 00 TP oo

oo

»o oo

CO lO CO 00 O 00 O CO O CD "O O CM O

00 rH

Tft CD

rH O OO o o oo 1^ o o oo oo oo

Cvl Tt* rH

CM Tt* CO *0

00 O CO o

OS O 00 CM OS CM eo >o CO oOS CMlO co,r^ O ^Ooo

»0 O »0 (O CO o

CO rH

rH CS CO CM oo 00 do 00 CO

i-H CM CM CO OOCO O 00 ^ rH CM

CM eo CM o CM O cq o tM O CM O CM O CM O CM O CM O CM O +-'

o o oo oo oo oo oo oo oo o o oo +^

00

rH

t'. »o rH CD

CO rH 38S OSco'd

O O I> rH rH r>. rH rH r- CM CO

© CM O CM O CMo CNJ O CMO

lO Ol o^

<N O

» CO ^ 00 40 o o eo f-( ^ ^ OS (N CO w

c^o c^o

w

CO lO O OS

lO O CD rH O 00 O 00

rH b- ^ ^ eo rH

CO CD CO

CD OS

rH CO

to t-- -H O CMO CM O rH O rHO rH O CM O

w w

w w w I I

rH CM r-t CM

30
Table 5-4. Calculated contribution of independent variables

to the 7-day heat of hydration

Independent

variable Range of variable

Coeffi- cients from

equation

6, table

5-2

Calculated contribution to HH(7)

Calculated range of contribution to HH(7)

CsA - 0 to 15 % +2. 10 0 to +31.

5

31.

5

C3S..-- -- 30 to 70 % +0. 68 +17. 4 to +40.

6

23.

2

C2S - - 5 to 50 % +0. 04 +0. 2 to +2. 0 1.

8

CiAF 4 to 17 % +0. 18 +0. 7 to +3.

1

2.

4

KjO 0 to 1.1 % +6.

1

0 to +6.

7

6.

7

SO3 1.2 to 3.e % +3.

7

+4. 4 to +13.

3

8.

8

Loss 0.3 to 3.e % -4.

1

-1.2 to -14.8 13.6 AIT JP ^CUl /g^ 2500 to 5500 +0 0048 +12 0 to +26.

4

14.4 Cu - 0 to 0. 05% -82 0 to -4.1 4.1 Cr 0 to 0.02% +224 0 to +4,5 4.5 Zr 0 to 0.5 % +21 0 to +10. 5 10.6 P... - 0 to 0.5 % -8 0 to -4.0 4.0

included, does not, of course, mean that the actual

contribution of the compound to the heat of hydration has changed, but that the information about

that contribution has changed. For example, eq

4, table 5-2, with only the four compounds results in a pretty good prediction of the heat of hydration, but in eq 5 the prediction due to eight variables is even better, as shown by the reduced S.D.,

and C4AF is here taking an inetfectual part in the

prediction in conjunction with the other seven

variables. In eq^6 the ability to predict is still better with both C2S and C4AF giving a negligible

contribution.

Using the same variables as were used for all the cements in eqs 3 and 6, the equations for the

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

in the relationships 3A and 3B for the AE -I- NAE

cements and 6A and 6B for the NAE cements. The C2S, C4AF, K2O, Cu, and Zr had coef,/s.d.

ratios less than 1 in either the "odds" or "evens"

or both. As indicated in previous sections, this

may occur when the coef./s.d. ratio is not signifi- cant in the equation for all the values, or 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.

In table 5-3 are presented a similar series of

ecjuations using the oxides present in major quantities instead of the potential compound compositions. The S.D. values obtained in this series of

equations do not differ appreciably from those pre- sented in table 5-2. The use of the major oxides

in eqs 1 and 4, resulted in highly significant reduction in the S.D. values. As in table 5-2 the use of

other commonly determined variables resulted in a further significant reduction, and the use of the

minor constituent resulted in a still further reduction in the S.D. values. The coefficients of the

major oxides, table 5-3, were not affected to so great an extent as were those of the C2S and C4AF

in table 5-2 by the addition of other variables. In

table 5-3 eqs 3A and 3B, or 6A and 6B, for the

"odds" and "evens" instances occurred where the

K2O, SO3, Cu, and Zr had coef./s.d. ratios of less than 1.

Table 5-5. Frequency distribution of cements with respect

to heat of hydration at 28 days

Heat of hydration, calories per gram

60 66 60 66 70 75 80 86 90 96 100 106 Type cement to to to to to to to to to to to to Total

65 60 66 70 75 80 86 90 96 100 105 110

Number of cements

I _._ 6

14

173

3

1 16

13

23 "223

3

2

6 5 1 80

7

16

1 48

1 19

116 188

lA

2 3 IIA*

II _ 2 13 14 3 IIA.

Ill _ 2 3 4 3

1

1 3 IIIA IV &V 1

1 11 711 319

3 Total 30 44 31 32 9 6 4

*0riftlnally classified as type I or lA.

In table 5-4 are presented the calculated contributions and ranges of contributions to the 7-day

heat of hydration. The coefficients of the independent variables of equation 6, table 5-2 were

used together with the approximate range of the

values for the different variables for the cements

used in this study. K2O and SO3 content and fine- ness appear to have had an appreciable effect on

the 7-day heat of hydration. There is also an indication that an increase in Cu, P, or loss on ignition was accompanied by lower heal: of hydration values, whereas an increase in Cr or Zr content may

be associated with an increase in the heat of hydration.

4.3. Heat of Hydration at 28 Days

The frequency distribution of the 28-day heat

of hydration values obtained on the cements of the

different types is presented in table 5-5. The dis- tribution of values with respect to the different

types was similar to that obtained at 7 days and

presented in table 5-1. In table 5-6 are presented selected equations re- lating the 28-day heat of hydration to various

independent variables. The use of the four major

potential compounds, as in eqs 1 and 4 resulted in a highly significant reduction in the S.D. value.

The use of loss on ignition and fineness in eqs 2 and

5 reduced the S.D. further, and a further significant reduction was attained by the use of the minor

constituents SrO, Cu, Co, Zr, and P as noted in eqs 3 and 6. (See also table 5-13.) In preliminary

trial equations the SO3, KjO and Cr, which had an

effect at 7 days, were found to have no significant

effect on the 28-day heat of hydration. The equations computed for the "odds" and "evens", equations 3A and 3B or 6A and 6B, indicated that the

relationships of Cu, Co, and Zr with 28-day heat

of hydration may be questionable.

In table 5-7 are presented a similar series of

equations using the major oxides instead of the

potential compounds. Tlie S.D. values in table

5-7 are comparable to those in table 5-6 and again

31
"(tl ep t-- CO O OS CO

U3 C4 Ol GO 00

JO CO +^ -H- ^ <S

1^7^ Io o. r» CO CO

OS i-t CO 0(5 c5 F o ^ lo t>; c 7- 7- r

ii ss ss

lO CO CO O OS

l-H CO F 00 o o 00 00

00 CD OS CD c5 01 CO

l-H OS CD

CD CDOS NO NO coo N rH

?5

00

CO

CO 00 0 CO

00 CO

1 1 ^ 00-*

+ +^

CO CO

N CO O O (M CO i-H GO GO

*0 ^00 O •O CM O CO COCO

00 CO CO »OCO cdci

C4 CO t O -*! CO ^ GO O 1-H N

N CO OS CO CO OS

CO l-H OS Is i§

00 00 00 00

^ OS

CO --H OS OS

80

*0 CO

00 ^

D CD coco rH 00 eOiC Sc5 ^ co

»0 to Cl W CO Of-H <-HC^ osc5 00 00 ^ o ^o

00 ^

0*0

00^ 00 +^ +^ +^ -HO ^ o

Tf< i-H OS N 00

SS

SIS

(M CD N o

CD »0 CO O I-H

c^) CO 00 o «-H >0 3? Tf CO CO CD O NO NO

OS OS

CON ^O SoO O CD NO CO O

o o 00 00 00 00 00 00 00 00 00

CO l-H Nco ^500 coop ^CO OS CON N »o OSiO 003! O —

t>. O t>. O !> O

S 5 3la l-H

o o N . -co . 00 ^ i-H>-^

»-l N 10

10 CO r- OS COT

CO CO O 00 l-H to

l-H ' N ^ iO CD + + +^

rH l-H O ^

lO

lOTj;

T»( N

I ^

l^OS N N NO

CD *0 7""CO

I ^

N 00 l-H CO N OS »oo T-i l-H NO N l-H COi-H ss ss ss

00 00 o o 00

kO N CO l-H CDO

CO OS N Cp l-H tT-H CO O 5 coo

CO o N l-H

I ^

CO rH » 1-H coco (> ^ ^

osco OS kO O + +^ +

rH ^ rH

to iO coo si

I

rH 10

osr-i CO'^ rH

»H O

CO

CO-* 7"" rHW

coo

I ^

^c<i OS OS Oa (O

CO Tf< t>. i>- CD 00 r- coo

I ^ CO O CO o coo coo

06 Tj« co'o

I ^

CO to ^

CD l-H O CO rH O rH OS OS N rH l-H CD rH CO N ^ N NON

OOP

CO N

CO O ^ o

^ c3 o

* 2S S N " N O N O N O NO N O N O +-' N O N O

N O

I ^ N OI N O! ^ N O

I ^ N O

I ^

CO

ui cc5

00

n"

**** y^. 7

N CD 7""

coo

I ^

coo coo coo eoo

N O

NO CQrH t-- OS t- CO ON O OS 0 00 rH C0»0 NCO U5CO N 0> »0 00 CO »0 W3 O ^l O eo-^ lOcD coco t^-* ^ CO coco iocd N O

I ^

CO N O N »0 rH

Eh

9

CO 00 rH rH 5N 1-! O rHCO OCO 50S ON t- C<) osco lO rH

5 rH CO r-1 »0 rH l>. rH CON N O N O N O N O N O NO N O NO N O IN O

SI

w

w

II II

w

t3l w w

N 10 CO *0

»o r- N U3»0 N 10 Ot^

CO »o SN rH rH NO r- 00 CO N 10 »0 !> O

N O COO NO NO NO +^ +^ COO coo +-

a

n

II II It II Sm 'dm W £, WII II II

13 q

w

w

rH N 32
Table 5-8. Calculated contributions of independent variables to the 28-day heat of hydration

npffi fi- Calcuents Calculated con- lated IndspGndcnt Range of from tribution to range of variable variable equation HH(28) contri6, table bution to

5-6 HH{28)

CsA 0 to 15 % +2.

8

0 to +42. 0 42. 0 CsS 30 to 70 % +0. 79 +23. 7 to +55.

3

31.6 CaS 5 to 50 % +0. 26 +1. 3 to +13.

0

11. 7 CiAF 4 to 17 % +1. 07 +4. 3 to +18.

2

13.9 Loss... 0. 3 to 3. 6 % -3.02 -0.9 to -10.9 10.0 APF (cmVg)— 2500 to 5500 +0. 0032 +8. 0 to +17. 6 9.6 SrO 0 to 0. 4 % -12.4 0 to -5.0 5.0 Cu 0 to 0. 05% -143 0 to -7.2 7.2 Co 0 to 0. 01% -503 0 to -5.0 5.0 Zr 0 to 0. 5 % +15.6 0 to +7.8 7.8 P 0 to 0. 5 % -8.1 0 to -4.0 4.0

Table 5-9. Frequency distribution of cements with respect

to 1-year heat of hydration

Heat of hydration calories per gram

80 85 90 95 100 105 110 115 Type cement to to to to to to to to Total

85 90 95 100 105 110 115 120

Number of cements

I 2 53

3

17

15

18

25

12

12

2

2 63

7

12

1 35

1 14

16 140

lAn* 2 HA* n 10 17 IIA 1 m 3 3 3 5 niA 1 IV & V 11 317

2 Total 31 35 31 17 6 2

•Originally classified as type I or lA.

indicate the effect of loss on ignition and fineness as well as the trace elements. ( See also table 5-13.)

The calculated contributions to the 28-day heat

of hydration together with the calculated ranges

of such contributions are presented in table 5-8. It may be noted that the effects of CgS and C4AF

are greater than they were at 7 days. This also

appears to be the case with loss on ignition and Cu

whereas the opposite may be noted for the effect of

fineness and Zr.

4.4. Heat of Hydration at 1 Year

The frequency distributions of the 1-year heat

of hydration values are presented in table 5-9. The distributions for the different types of cement

overlapped to a greater extent than was noted for

the 7- and 28-day heat of hydration values.

In table 5-10 are presented the computed equations relating the heat of hydration at 1 year to various independent variables.

By using only the major potential compounds

as in eqs 1 and 4 of table 5-10, there was a signifi- cant reduction in the S.D. values. When such

other ordinarily determined values as Na20, loss on ignition, and fineness were included (eqs 2 and

5) the S.D. values showed a further significant

reduction. It may also be noted that by using the

trace elements Cu, V, Ba, and P in the computed

e

Si

S S

CO ^ -^00 CO

CO -I CO CO

CO

I ^

N o> 00 i-H r- «o ^ 03 CO to CO

t-c CO CO SO CO «5

o o o o +^

O CO ^ 00 00 o o

o o

I>- CO

to c5 CO as w eo

!N O

I ^

OS —

<

O OS «o o to!N 00 (N ^

C-1 »-<

CO

gC-J »n O CO

-"J" oi CO V CO CO

CO

C5 QO co^' +^

00 O CO WW »0 CO +^ 4.-

r-- CD

(N O o o

too oo

o o 00 00

SC3S

lO to

CO a> CO CO to OJ

CO OS

(M o MO NO

(N OS

1

to »Q CO o to 0

CO 01 o

>0 O CO

CO lO lO lO CO <N C» *-i OS (M CD ?N U3 ^ COO

i-H to WOO CO to lO >-H OS (N CN uD CM OS OO cO w 00

OS to 10 OS »0 CD O CO CD O to tO lO COCO

CO >-H to '-H r- i-H toc^ r-fM tow tow -h c^c^ 00 o"o 00 cJo' 00 o'o o"o o'o 00 00 +" +^ +- +^ +" +'-' +"^ +^

tooo OS CO ^ CO 5^" ci^ TP o COO S" coo

00 1- toio Tfi to -H-^ w coo tor- cs go to* com o OS'S' r-. T}< lo CD or- *o »—" os-^ 1—1 m woo coo lo o 100 too »o o CO o too lO o too 00

crJo 00 00 00" 00 oc) 00 00 c>o' 00 +" +^ +" +^ +^ +^ +" +'^ +^ +^

»0»0 COt>- -^tO GOi—t CQiO OCO t—OO OtO OtO tOf^ coco CO Of- to to CO to O lO COCO wo 00 00 00 00 WO 00 00 00 wO

wo w" O w* O' wo w' o w" O w' O wo* w O w cJ +^ 4.- 4.- 4.-

TP eoS^ 00 <N co" oS? t-o" co lO 00 lO cd ic cow cow CO (N CO CO 00 as (M r- w co c^i r- 00 as cow cow cow w Tf" w w (M w CO w w CO w o o o' ci c3 c4 o o o co' o cs' o cs o +'-' +"" +"" +"" +"" +^ +"" +'-' +"" +'•"

II II II II II II II II II II II ll_ II ll_ II 11^ II 11^ II II Ct) C'O ^-d 'a'd Cxj C-d Ct3 S^xi 'a'd S<n C-oi IrtM Om god C,o5 w,"

9 a 3 k

33
D.

CO QO O O «N GO

CO -^1-1 I CO

CO i-H w^lO

C50 (M CO

o oo

CO r- CO 00

CO O CM -—I CM >—

<

o o o o o o o o o o o o

o o oo

OCS) CO

CO CO

CD (M'

OS t>- lO CO I-H ^

CO ^ ^ oi o ^'

CO lO 1-H N

^ N CO i-HCO CO N 1-H C4 »0 CO +^ +^ +^

OS »0 O 00

»CO0 O-^ OOCO CO lO

I-H o oo CO I-H !M O <N O CO ^ O --H oo oo oo oo OO oo

o o o o o o oo

<N r- <N CO CO 1-H O CO o t-- CD CD GO CO OS

O O O OS O tN lO CO CO O <M OS

iM OS CO GO 't* OS

I +

CO

lO CO CM OS o OS 00 t-- »c

t-~f£) lO CC^ CM "O

CD CM *C 00

CO 00

CO o

I ^

00 CO

CD I-H

CO

00 r-l CO (N

CO CO t-- o CO eo 00

CO CO I-H

00

00 1-t CO

00 o »c CO O 00

1-H M

CO OS

r- CO

CM O CM O CM O CM O C3 O o CM O C<) o CM O c^ o

in 1-H o o OXw-* CM O oo 00 TP OS CO lO oo O CO

OS OS 00 CD O

I ^

C<1 OS CO 00 O

CM CO

os ^

eo 00 00 !>. O OS

OS CO

»0 OS ^ o 1-H O O ^ o o

II II II II II II

> w

9'^

t3 w

Table 5-12. Calculated contributions of independent

variables to the 1-year heat of hydration

Coeffi- Calcucients Calculated lated Independent Range of variable from contribution range of variable equation to HH(IY) contribu6, table tion to 5-10 HH(IY)

CsA 0 to 15 % +2.33 0 to +34.

9

34.

9

C3S - 30 to 70 % +1. 06 +32. 8 to +74.

2

42.

4

C2S --- 5 to 60 % +0. 60 +3. 0 to +30.

0

27.

0

C4AF. 4 to 17 % +0. 76 +3. 0 to +12.

9

9.

9

Na20 0 to 0. 75% -5.33 0 to -4.0 4.0

0.3 to 3.f % —2. 55 —u. 0 to —y. ^ 8.

4

APF (cmVg)- 2500 to 5500 +0. 0026 +6. 5 to +14.

3

7.8 Cu 0 to 0. 05% -119 0 to -5.9 5.9 V 0 to 0.1 % +43 0 to +13 4.3 Ba 0 to 0.2 % -37 0 to -7.4 7.4 P - 0 to 0.5 % -7.2 0 to -3.6 3.6

Table 5-13. "F" values for significance of reduction of variance due to added variables.

Critical J?" Table Equations "F" ratio D.F.

a=0.01 a =0.05

*0, 1 102.

3

4:168 3.45 2. 45

5-2 1> 2 17.

4

4:164 3. 45 2.45

2, 3 6.4 4:160 3. 45 2.45

5-2 **0, 4 96. 0 4:158 3 45 2. 45

4, 5 16. 8 4:154 3. 45 2. 45

5, 6 6.2 4:150 3. 45 2.45

5-3 *0, 1 114.

0

4:168 3.45 2.46

1. 2 13. 0 4:164 3.45 2.45

2, 3 6.4 4:160 3.45 2. 45

5-3 **0, 4 107.2 4:158 3.45 2.45

4, 5 12.6 4:154 3. 45 2.45

5, 6 6.2 4:150 3. 45 2.46

5-6 •0, 1 108.9 4:168 3.45 2. 45

1, 2 8.6 2:166 4.75 3. 05

2, 3 7.5 5:161 3.13 2.28

5-6 **0, 4 101.9 4:158 3.45 2.46

4, 5 8.0 2:156 4. 75 3.05

5, 6 7.8 5:151 3.12 2.28

5-7 *0, 1 110.0 4:168 3. 45 2.45

1, 2 6.8 2:166 4.75 3.05

2, 3 7.7 5:161 3. 15 2.28

5-7 **0, 4 103.4 4:158 3.45 2.45

4, 5 6.2 2:156 4. 75 3.05 5,6 8.1 5:151 3. 15 2.28

5-10 *0, 1 69.2 4:123 3.50 2.45

1, 2 8.5 3:120 3.95 2.68

2, 3 5.1 4:116 3. 50 2.45

5-10 **0, 4 63.2 4:113 3.50 2.46

4, 5 8.8 3:110 3. 97 2.69

5, 6 5.4 4:106 3. 50 2. 46

5-11 0, 1 73.7 4:123 3. 50 2.45

1, 2 7.2 3:120 3. 95 2.68

2, 3 4.8 4:116 3. 50 2. 45

5-11 "0, 4 67.3 4:113 3. 50 2. 45

4, 5 7.5 3:110 3. 97 2.70

5, 6 5.2 4:106 3. 50 2.46 AE+NAE cements. *NAE cements.

eqs 3 and 6 a further significant reduction in S.D.

values was attained.

The equations for the "odds" and "evens" in the

array of cements indicated that Cu, V, and Ba had

coef./s.d. ratios less than one in some instances.

By use of the principal oxides as in table 5-11

instead of the potential compounds as in the pre- vious table similar results were obtained. The use 34
of only the principal oxides (eqs 1 and 4) resulted

in highly significant reductions in the S.D. values.

As also presented in the previous table, the use of

NaaO, loss on ignition, and fineness (eqs 2 and 5) or these variables with the addition of the trace elements Cu, V, Ba, and P (eqs 3 and 6) each re- sulted in significantly lower S.D. values.

For the equations computed for the "odds" and

"evens" (3A, 3B, 6A, and 6B) there were instances

when the Cu, V, Ba, as well as fineness had

coef./s.d. values less than one. In table 5-12 are presented the calculated contributions of the various independent variables to the 1-year heat of hydration as well as the cal- culated ranges of contributions for the different

variables.

5. Discussion

5.1. Age of Test Versus Trace Element Effect

The minor and trace elements which apparently

had effects on heat of hydration were not always

the same for the different ages. Some were significant at some ages but not at others, and the

coef./s.d. ratios of some were different at different

ages (see tables 5-2, 5-6 and 5-10; also 5-3, 5-7

and 5-11) . Reference will be made specifically to the equations for the NAE cements in these tables. The loss on ignition, air permeability fineness, and

P were highly significant at all ages and were consistent with published information relative to their

effects. In the equations for the relationship between 7-day heat of hydration and major compoimds, the coef./s.d. ratios for K2O, SO3, Cr, Cu,

and Zr were also highly significant. Where the

major oxides were used in the equations this was

also true except for the SO3 which was of questionable significance. In the equations for the 28-day

heat of hydration both with compounds and with

oxides, the coef./s.d. ratios for K2O, SO3, and Cr

were less than one and therefore do not appear.

The ratios for SrO and Cu were significant at the one percent level and that of Co at the five percent

level. The significance of Zr was less at 28 days

than at 7 days, whereas the ratio for Cu became more significant. In both sets of equations for the one year heat of hydration the coefficient for NajO

was highly significant and had a negative value,

whereas K2O which was the significant alkali and

had a positive coefficient at 7 days, was not significant. The coef./s.d. ratios for SrO, Co, Cr and Zr

were all less than one in preliminary equations and

therefore do not appear in the tables. V and Ba

appeared significant in the 1-year equations with

the potential compounds and less significant when

the calculations were made with the major oxides.

5.2. Effect of Minor Constituents and Trace

Elements on Calculated Coefficients of

the Major Calculated Compounds

Data from different sources showing calculated

coefficients for the effects of the major potential

compounds on heats of hydration at different ages

are plotted in figure 5-2. The plotted points at the midpoints of the vertical bars represent the

calculated contribution of the compounds to the

heat of hydration in terms of calories per gram.

and the ends of the bars represent the 95-percent

confidence limits.* Bars (1), (2), (5), (6), (9),

and (10) in each part of figure 5-2 represent data

from this investigation taken, respectively, from

equations (4) and (6) in tables 5-2, 5-6, and 5-10.

FIG. 5-2 A C3S

T

1 ii

1 a. i.

"

1

1

1 1

1 1 i 1 J.

(1)12) (3)M) 15)(6) (7X8) (91(10) (1002)

7 DAY 28 DAY 1 YEAR

FIG 5- 2 C C3A

ti

FIG. 5-2 B C2 S O NBS" 4 VARIABLES A NBS« ALL VARIABLES A PCA 4 VARIABLES PCA 5 VARIABLES • LERCH-BOGUE

(PURE CPDS) tNAE CEMENTS

ii

I

I J.

(I)(2) (3)(4)

7 DAY

(5KS) (71(8)

28 DAY

(9X101 01X12)

I YEAR

FIG. 5-2 D CAF

O NBS' 4 VARIABLES A NBS« ALL VARIABLES A PCA 4 VARIABLES

PCA 5 VARIABLES • LERCH-BOGUE

(PURE CPOS) -NAE CEMENTS

t6

FiGUKE 5-2A, B, C, and D. Heat of hydration in calories per gram at 7 days, 28 days, and 1 year for CsS, C,S, CsA, and dAF.

« The 95-perceiit confidence limits represent limits computed

from the data such that 95-percent of limits so computed (from

sets of similar data) will bracket the true value of the coefficient. See, e.g.. M. G. Natrella, Experimental Statistics, NBS Handbook

91, pp. 1-11 to 1-13 (1963), U.S. Government Printing Office.

35
The other bars are taken from other published data

and will be discussed further in a later subsection.

In this and subsequent subsections based on

figure 5-2, the following statistical criteria will

be followed: (1) A highly significant difference

between two coefficients (whether these represent

different ages of test or the same age with and

without additional variables) is indicated if the

95-percent confidence limits of the two coefficients do not overlap; (2) a frobable difference between

coefficients is indicated if they differ by more than

three times the standard deviation (s.d.) , provided

that the two s.d.'s are approximately equal; (3) no difference between coefficients is demonstrated

if one of the two coefficients lies within the 95-

percent confidence interval for the other coeffi- cient, unless there is other evidence supporting the

assumption of a difference.

Bars (1), (5), and (9) in figure 5-2 represent

equation (4) in the three tables in which only the

four major compounds were used as independent

variables, while bars (2), (6), and (10) represent

equation (6) in which a number of other variables were also included.

At the age of 7 days a highly significant reduction in the coefficient for C3S was caused by inclusion of the additional variables, and a probably

significant reduction occurred for C2S and C3A.

At the other two ages for these three varialbles and

at all ages for C4AF, no significant difference was

indicated.

5.3. Numerical Values of Coefficients of the

Major Potential Compounds at Different

Ages of Test

Comparing the coefficients obtained at the differ- ent ages, bars (2), (6), and (10) in each of figures

5-2 A, B, C, and D, the coefficient increased significantly with age of test for both C3S and C2B.

The increase was highly significant for all but the

28-day to 1-year increase for C3S, but even in this case the overlap between confidence intervals was

quite small, and the evidence for an increase is strong.

For C3A and C4AF a highly significant increase

occurred between 7 and 28 days. Between 28 days

and 1 year, however, there was a probably signifi- cant decrease for C3A and no evidence of a signifi- cant change for C4AF,

5.4. Comparison of Coefficients of Major Potential Compounds Obtained in this

Investigation With Previously Reported

Values

Also presented in figure 5-2, parts A, B, C, and

D are coefficients relating to heat of hydration re- ported by Verbeck and Foster [10] of cements of

the Portland Cement Association (FCA) long

time study of cement performance. The values

used in this comparison are those reported for the

12 cements hydrated at 70 ° F and for which least squares computations were made using only the

four major compounds (bars (3), (7), and (11)

in figure 5-2) and the four major compounds

plus SO3 (bars (4), (8), and (12) in figure 5-2).

The PCA data was presented in the original paper

together with plus or minus values to indicate

probable errors which would correspond to approximately a 48-percent confidence level for the

number of tests involved. These values were re- computed in terms of the 95-perc6nt confidence

level taking into account the number of degrees of

freedom. (The values were verified by recalculating the PCA values by means of the computer.)

The lengths of the bars (3), (4), (7), (8), (11),

and (12) in figure 5-2 represent the recalculated

95-percent confidence limits for the PCA data

with and without SO3 as a variable.

In general, comparisons between coefficients in the PCA studies and in the present investigation were difficult because of the wide confidence intervals of the former resulting from the small number of tests. There were significant differences,

however.

For comparisons of coefficients in equations in- volving only the four major compounds (bars (1)

and (3), (5) and (7), and (9) and (11)) the confidence intervals overlapped in all 12 cases. There

were only two cases where the evidence indicated

a possible difference, viz, C3A at 7 and 28 days.

In these two cases the coefficient for the NBS data

appeared to be lower, indicating a lesser effect for

this variable than was found in the PCA data.

With SO3 as an added variable with the PCA

data and a larger number of added variables in

the NBS data, highly significant differences were

indicated at the age of 1 year for C3A and C4AF

and probably significant differences at the same

age for C3S and C2S. The coefficient obtained

with the NBS data was lower in each case. For

the other two ages, no difference in coefficient between the two studies was detected.

In addition to the wide confidence limits of the

PCA data caused by the small number of cements

tested, some other factors need to be taken into

consideration in comparing the two sets of data.

The PCA values included only cements with 1.0 percent or less ignition loss which was not the

case with the NBS values. There were also slight

differences in test methods and basis of reporting

(ignited versus unignited weight of cement) which

may have resulted in some differences in the re- ported values.

Woods, Steinour, and Starke [8] have also given

coefficients for regression equations using the four

potential compounds and the four principal oxides

calculated on the results obtained from 13 laboratory prepared cements. The pastes were stored at 35 ° C (95 ° F) during the hydration period as compared to 23 ° C (73 ° F) required at present.

Their equations for 25-day results are as follows:

36
HH(28) =

s.d.=

S.D.=

2.02 C3A+I.I4 C3S +O.44 C2S +O.48C4AF

(0.30) (0.081) (0.067) (0.28)

3.80

HH(28)= 3.31 CaO-4.93 SiO -3.1 FeaOs-O.l AI2O3

These may be compared, respectively, to eqs 4 in

tables 5-6 and 5-7. Agreement is quite good ex- cept for AI2O3 and C4AF. The s.d.'s and S.D. were calculated from probable < rrors given by the

authors. They did not report the probable errors for the second equation with the oxides.

Woods et al., also reported on the relationship

between heat of hydration at various ages and the

function, % C3S + 2.1 X % C3A. This simple function, which was calculated on the assumption that

the contributions of C2S and C4AF were small and

equal, was claimed to be "a useful one for quick

rough approximation of the relative standing of

two cements differing only in composition" (italics

ours). The author recognized that the application of the results of their analysis to commercial

cements should not be expected to produce as good

agreement between calculated and experimental

values as was obtained with their laboratory-prepared cements.

Plots of the heats of hydration obtained at 7 and 28 days and 1 year in our investigation versus the function % C3S + 2.1% C3A are given in fig- ures 5-3, 5-4, and 6-5. The correlation is quite

good. The regression equation obtained from our

115 -

data for the 1-year heat of hydration was as follows

HH(1 yr) =58.87 -fO. 52 C3S-f 1. 54 C3A

s.d. = (2. 85)(0. 053) (0.12)

The S.D. for this equation was 3.909, compared to 7.031 for the heat of hydration values. The ratio

of 2.9 to 1 in the above equation for the contribution of C3A verus that of C3S, compares with the

ratio of 2.1 to 1 given by Woods et al.^ This difference may have been due in part to the differ- ence in curing temperature.

Lerch and Bogue [6] and Thorvaldson et al. [7] have reported values for heat of hydration of

the major potential compounds in portland ce- ments, and Lea and Desch, [1, p. 246] quote Brisi

[21] as having obtained values of 125 and 63

calories per gram for the heat of hydration of

C3S and C2S, respectively. Comparing the values

which have been reported with the coefficients obtained in the present study for the 1-year heat of

^ The function given by Woods et al. was obtained by averaging

the heats at the various ages for each compound, subtracting the mean value of the heat for C2S and C4AF from the values for

C.-iS and C3A, and adjusting the values for C3S and C3A to a basis

of 1.0 for C3S, maintaining the ratio of 2.1 to 1 between the two.

100

O 85

70

55

40

10 20 30 40 50 60 70 80 PERCENTAGE C3S + 2.1 TIMES PERCENTAGE C3A 90 100

Figure 5-3. Eeat of hydration at 7 days versus the quantity {percentage CsS-f-S.iX percentage CaA).

37
hydration (bar (10) of figure 5-2) it may be noted

that the numerical values and 95-percent confidence limits for C3S and C4AF are below the re- spective values of 120 and 100 cal/g reported by

Bogue for these compounds. The value for the

coefficient for C2S is close to the value of 62 cal/g

reported by Bogue, and the value for C3A is not

significantly different from the value of 207 cal/g

reported by Bogue or the value of 214 cal/g re- ported by Thorvaldson.

5.5. Heat of Hydration and Compressive

Strength

It has previously been reported [10] that there was a correlation between the heat of hydration

and compressive strength of cements at early ages

but not at later ages. A study of variables associated with compressive strength will be presented

in a later section of this series of articles. However, table 5-14 presents some computed relationships between the heat of dydration at 7 and 28

days and 1 year versus the compressive strengths

of water-cured 2-inch mortar cubes at the respective ages. The "F" values are the ratios of the

reduction in variance due to the fitted constants

associated with the independent variables to the

variance obtained from the residuals after fitting

the constants. At 7 days there was a significant

relationship between the heat of hydration and

strength. At 28 days the reduction in variance was somewhat less but still highly significant

whereas at one year there was no apparent corre- lation between the heat of hydration and compressive strength.

6. Summary and Conclusions

(1) Studies were made of the dependence of the

heat of hydration of portland cements on cement

composition, including minor constituents and

trace elements as well as major potential com- pounds and major oxides. Heat of solution tests were made at 7 days, 28 days, and 1 year on a

large number of portland cements of different

types and from different mills in different areas of the United States.

(2) Computations of multivariable equations by

a least squares method for air entraining and nonair-entraining cements combined or non-air-entraining cements alone indicated that a number of

independent variables are associated either di- rectly or indirectly with the heat of hydration of

the cements. The following observations relate to the results obtained with the non-air-entraining

cements in which the major potential compounds

were used as independent variables.

(2.1) The effect of C3S and C2S on the heat

115

100

85 -

70 -

55 -

40

10 20 30 40 50 60 70 80 PERCENTAGE C3S + 2.1 TIMES PERCENTAGE C3A

90 100

Figure 5-4. Heat of hydration at 28 days versus the quantity {percentage Ca8+2.1X

percentage O3A).

38
< 100 -

UJ

Q- " m I o

X

40 -

^ ^ ^ ^ _^ ^ ^ ^ 0 10 20 30 40 50 60 70 80 90 100 PERCENTAGE C3S + 2.1 TIMES PERCENTAGE C3A

Figure 5-5. Heat of hydration at 1 year versus the quantity {percentage CsS+^.iX

percentage O3A).

Table 5-14. Coefficients for equations relating heat of hydration to compressive strength at the respective ages and the resulting reduction of variance

Equation Type cement Const. Compressive strength S.D. "F" D.F.

Critical F

7d 28d a = 0.01 a =0.05

1 AE+NAE HH(7)= +46.24

s.d.= (1.96) +0. 00757(0. 00057) 6.90 86.9 2:170 4.7 3.0

2 do HH(28)= +53.90

s.d.= (3.36) HH(1Y) =+103.4

s.d.= (4.3) HH(7)= +44.38

s.d.= (2.02)

+0. 00584

(0. 00065)

7. 63 40.4 2:180 4.7 3.0

3 do -0. 00089 6.96 0.9 2:133 4.8 3.1

(0. 00068)

4 NAE +0. 00801

(0. 00069) 6.72 93.5 2:160 4.7 3.0

5 do HH(28)= +48.96

s.d.= (3.67) HH(1Y)=+104.2

s.d.= (5.1)

+0. 00671

(0.00068) 7.44 48.2 2:170 4.7 3.0

6 do -0. 00103 6.96 0.8 2:123 4.6 3.1

(0. 00079)

of hydration increased with the length of hydration. At 1 year it was slightly lower than previously published values for C3S and did not differ

significantly from those values for C2S. The heat

of hydration attributable to C3A and C4AF was

slightly higher at 28 days than after 7 days or 1 year hydration. All values were within reasonable agreement with previously published values.

(2.2) Of the commonly determined variables,

high loss on ignition was associated with low heat

of hydration and high fineness was associated with

high heat of hydration. High values for K2O

and SO3 were associated with high heat of hydration at 7 days, but not at later ages. High values

for NagO were associated with low values of heat

of hydration at 1 year, but not at 7 or 28 days.

39
The use of the commonly determined variables re- sulted in significantly better agreement between

calculated and observed values than was obtained

with the four compounds alone.

( 2.3 ) Of the other minor constituents or trace elements, increased values for Cu and P were as- sociated with lower values of heat of hydration at

all ages. The relationship with P was highly significant at all ages ; that of Cu was more significant at 28 days and 1 year than at 7 days. Increased

values for Cr and Zr appeared associated with

high heat of hydration at 7 days. At 28 days there was no evidence of a relationship with Cr, and the

significance of the Zr was less than at 7 days.

Neither of these elements was significant at 1 year. SrO and Co appeared associated with lower heat of

hydration at 28 days but not at 7 days or 1 year. At 1 year, increase in V appeared to be related to high heat of hydration and increase in Ba to low

lieat of hydration but neither of these elements

showed any effect at the earlier ages. The use of

the minor constituents and trace elements in the

equations together with major compounds and

commonly determined variables resulted in significantly improved agreement between calculated

and observed values.

( 3 ) Inclusion of the air-entraining cements with

the non-air-entraining cements did not greatly

affect numerical values or significance of the coefficients of the major potential compounds in the

equations* as compared to those calculated for only

the non-air-entraining cements.

(4) Using the major oxides resulted in a series

of equations which produced similar reductions

in S.D. to those obtained with equations computed

for the major potential compounds.

(5) The relationships between heat of hydration and a function of C3A and C3S were more dis- persed for the commercial cements of this study

than for laboratory prepared cements reported

in previous studies.

(6) It was verified that there was a highly significant relationship betw^een the heat of hydration at 7 and 28 days and the compressive strength

at these ages. There was no apparent correlation

between the heat of hydration at 1 year and the

1 year compressive strength.

7. References

[1] F. M. Lea and C. H. Desch, The Chemistry of Cement

and Concrete, revised edition (Edward Arnold

(Publishers) Ltd., London 1956).

[2] R. H. Bogue, The Chemistry of Portland Cement, 2d

edition (Reinhold Publishing Corp., 19.55). [3] H. F. W. Taylor, The Chemistry of Cements (Academic Press, London and New York 19f>4 )

.

[4] Proceedings of the Third International Symposium

•on the Chemistry of Cement, London 1952, Cement

and Concrete Association, London.

[5] Chemistry of Cement, Proceedings of the Fourth

International Symposium, Mono. 43, vol. 1, 2 Aug.

1962, U.S. Government Printing OflSce, Washington, D.C.

[6] W. Lerch and R. H. Bogue, J. Res. NBS 12, 645

(1934).

[7] Thorvaldson, W. G. Brown and C. R. Peaker, J. Amer. Chemical Soc. 51, 2678 (1929) ; 52, 80; 910; 3927 (1930).

[8] H. Woods, H. H. Stienour, and H. R. Starke, Ind. Eng. Chem. 24, 1207 (1932).

[9] R. E. Davis, R. W. Carlson, D. E. Troxell, and J. W.

Kelly, Proc. Am. Concrete Inst. 30, 485 (1934).

[10] G. J. Verbeck and C. W. Foster, Proc. Amer. Soc. for Testing Mtls., 50, 1235 (1950).

[11] Wm. Lerch, RP1127, J. Res. NBS 21, 235 (1938).

[12] R. W. Carlson and L. R. Forbrich, Ind. Eng. Chem.,

Anal. Ed. 10, 382 (1938).

[13] F. B. Hornibrook, G. L. Kalousek and C. H. Jumper,

J. Res. NBS 16, 487 (1936).

[14] Same as reference [5], p. 545. [15] Same as Reference [3] , p. 313-370.

[16] Same as reference [5] , p. 453-463.

[17] Interrelations Between Cement and Concrete Properties ; Materials and Techniques, NBS Building

Science Series #2, Part I, Section 1. [18] Interrelations Between Cement and Concrete Properties : Occurrence of Minor and Trace Elements

in Portland Cement, NBS Building Science Series #2. Part I, Section 3. [19] Federal Specifications SS-C-158c Amendment 1: Cements, Hydraulic, Methods for Sampling, In- spection and Testing, May 25, 1954.

[20] Standard Method of Test for Heat of Hydration of Portland Cement, ASTM Designation C-186-53.

[21] C. Brisi, Ric. ScL, 24, 1436 (1954).

40
Section 6. Variables Associated With

Small Autoclave Expansion Values

of Portland Cements

R. L. Blaine and H. T. Arni

x'he autoclave expansion values of the cements in this investigation ranged from minus

0.05 to plus 0.50 percent. Statistical analyses used to determine the variables associated with the expansion confirmed that MgO and CsA were most significant. Increased values

of the alkalies, SrO, V, and loss on ignition were also associated with higher autoclave

expansion, whereas increases in SO3 and Cr were associated with a decrease in the expansion values.

Contents

Page

1. Introduction 41

2. Materials - 41

3. Testing procedure 41

4. Results of tests 42

5. Discussion . 42

6. Summary and conclusions 44

7. References 44

1. Introduction

The autoclave expansion test has been used in

the United States as an accelerated test for soundness of Portland and other hydraulic cements for

a number of years. H. F. Gronnerman, William

Lerch, and Thomas M. Whiteside have presented an extensive review of the literature dealing with

the autoclave test and the variables associated with

the expansive characteristics of portland cements

[1].^ It is generally recognized that excessive

quantities of MgO in the form of periclase as well

as "free" lime in portland cements may result in

large expansions of the neat cement bars when subjected to the autoclave treatment and, also, may

cause excessive expansion and deterioration of

concretes stored at normal temperatures. The

potential tricalcium aluminate content of the cement has been reported as contributing to the ex- pansion in the autoclave test, but not necessarily to the potential unsoundness or later volume ex- pansion of concrete. It has also been recognized

that certain additions to the clinker such as pozzolans (see p. 54 of ref [1] ) may reduce the autoclave expansion of the cement to some extent. Unsoundness of portland cement is associated

with autoclave expansion values many times larger

than those obtained in this study. However, the

contributions of tricalcium aluminate and other

factors mentioned above may have a significant

effect when expansion values are close to the specification limits. Thus it appeared desirable and

feasible to evaluate the contribution of the differ- ent variables to the small expansion values obtained on these cements.

2. Materials

The portland cements used in this study are the same as those which have previously been described

in sections 1, 2, and 3 of part 1 of this series of papers [2] . These included 199 portland cements of

different types and from different areas of the

U.S.A., and a few from other countries.

3. Testing Procedure

Neat Portland cement pastes of normal consistency were tested in accordance with ASTM [3]

and Federal [4] specifications in effect for autoclave expansion of portland cement at the time the

tests were made.

The results of tests were analyzed statistically

using the same procedures described in section 1, of part 1 of this series [2] . Briefly this consisted

of determining by least squares relationships with

^ Figures in brackets indicate the literature references at the end of this section.

the principal variables and combinations of variables which were known to be associated with the

autoclave expansion of the different cements, and

then using various techniques to determine which

of additional measured variables appeared to have

a significant effect in improving the agreement of

actual values and those calculated by the equation.

As in previous sections, the 3 white portland

cements and the cement having a high autoclave

expansion were not included in the calculated

equations.

41
4. Results of Tests

The frequency distributions of the different

types of cements with respect to autoclave expansion are presented in table 6-1. It may be noted

that although an autoclave expansion of 0.50 per- cent was the specification limit at the time these

cements were manufactured, the majority of the

cements tested had an expansion of less than 0.10

percent. Most of the cements having 0.25-percent or more expansion were those classified as type I or type IA. Eleven of the cements had negative

values for autoclave expansion.

Equations relating the autoclave expansion

values to various independent variables are presented in tables 6-2 and 6-3 for the AE-f NAE

and the NAE cements respectively.^ In equation

1 of 6-2, with the use of C3A and (MgO) ^ as independent variables, there was a highly significant

reduction in the S.D. value.^ It has previously

been established that the use of the second power

of MgO resulted in slightly lower S.D. values than was obtained by using the first power (see for ex- ample eqs 4 and 5 ) . By use of the alkalies and SO3

as additional independent variables as in eq 2 there was a further highly significant reduction in the

S.D. value. (See also table 6-5 which presents

the reduction of "F" values as well as the critical values of "F" at the 0.05 and 0.01 limits.) The

addition of the variables, loss on ignition, SrO, V,

and Cr values for the cements, as in eq 3, resulted

in a further significant reduction in the S.D.

values. (See also table 6-5.) The use of' the

AI2O3 and FcaOs instead of the potential C3A content as in equations 5, 6, and 7 resulted in a similar

series of equations with coefficients and S.D. values

comparable with those of equations 1, 2, and 3

respectively.

The calculation of equations for the "odds" and

"evens" in the array of cements indicated a fair

degree of concordance as may be noted in eqs 7A

and 7B. It may be noted that for "Loss" and Cr

( coefficients of neither were very highly significant

for the entire group of cements, eq 7) the coef./s.d. ratio was less than one in table 6-2, eq 7A for the

AE + NAE cements. In table 6-3, eq 7B, the

coef./s.d. ratio of Na20 was less than one whereas

the ratios for Loss and Cr were greater than one. Some of the limitations of the methods of statisti- cal analyses used have been presented in previous

sections of this series. In table 6-3 are presented the equations relating

the autoclave expansion of the NAE cements to the same independent variables used in table 6-2 for

AE-I-NAE cements. Although there were a few

discrepancies as noted previously, the effects of the

few AE cements on the coefficients or the S.D.

values were not large.

In table 6-4 are presented the calculated contributions of the various independent variables and

the ranges of these contributions to the expansion

values based on equation 3 of table 6-3. As in previous sections these values must be added to the

computed constant and are estimates of the magnitude and range of the contributions of the differ- ent variables which may be expected with normal

Portland cements. Slightly different values would

be obtained by use of other equations.

5. Discussion

Expansion values obtained on any sample of ce- ment are usually quite reproducible. It has been

reported that the rate of cooling of the cement

clinker can greatly affect the expansion values ob-

^ Abbreviation and notations used in this section are consistent with those used in previous sections. For example AB-I-NAE

refers to the air-entraining plus the non-air-entraining cements, CsA refers to the potential tricalcium aluminate and "Loss" to the loss on ignitipn. In addition "Exp" is used in equations to signify the percentage autoclave expansion.

3 The statistical terms used in this section are consistent with

those used in previous sections. For example S.D. refers to the

tained [1]. The rate of cooling of the cement

clinkers may differ in different mills, and this is probably one of the factors which masked the contribution of some variables to the volume changes

estimated standard deviation calculated from the residuals of a

fitted equation, or the estimated standard deviation about the

average. Also as In previous sections, s.d. refers to the esti- mated standard deviation of the coefficient of an independent

variable used in a fitted equation, coef./s.d. the ratio of the esti- mated coefficient (of an independent variable used in an equation) to its estimated standard deviation, and "F"= Fisher's

ratio of variances. Table 6-1. Frequency distribution of cements with respect to autoclave expansion

Type cement

Percentage autoclave expansion

-0.05 to Total

0

0 to 0.05 0.05 to

0.10

0.10 to 0.150.16 to 0.200.20 to 0.26

0.25 to 0.300.30 to 0.350.35 to 0.400.40 to 0.450.45 to 0.50

0.50 to 0.55

Number of cements

I 9 15 1738

2

1

13

36

10

12

10

12

7

1 41 3 3 3 81

8

673

203

15 197

lA 1 n 3 35 16

18

2

1 IIA ni 4 6 1 IIIA IV & V 4

11 8 Total 68 42 13 13 9 5 4 3 3 1

42
il

i!

+

m si il

76 -fd 7s

il il Si

^is $2- qis

il

$0

il il il

00 00 00

ii ii ii

00 00 00

is is IF^s il il il

00 00 00 00

ii if il il

00 00 00 00

0= °s

il il ii il

== OS

il il il I il il il il M

0= 00 00 00 °o 00 0= 00

ii=s

i ;

i \

I I il il il

°S 00 00

i i

\ il il il ii il ii

;

il il il il il Ii

00 00 00 oo- 00 00

il If il II if il ii il if

00 00 00 00 00 00 00 00 00

i I

n 11 ,11

-h'M MM

V

M»'

1 1 1 1 i i 1 i i

0 0* 0 0 0 o* 0 0 0

1

-2.643 (1.404)-2.661

(1.411)

-2.

609

(1.993)

-2.

724

(2,

190)

>

+1.086 (0.

344)

+1.084 (0.

349)

+0.

822

(0.

499)

+1.218 (0.

525)

1 +0.

2601

(0.

0724) i

+0.

2606

(0.

0737)

+0.

3561

(0.

1207)

+0.

2357

(0.

1104)

1

+0.

0213

(0.

0110)

+0.0214

(0.0111)

+0.

0296

(0.

0211

+0.

0186

(0.

0143)

i

-0.

0258

(0.

0179)

-0.

0478

(0.

0181)

-0.

0259

(0.

0180)

-0.

0478

(0.

0183)

-0.

0616

(0.

0278)

-0.

0349

(0.

0268)

i

+0.

0820

(0.

0294)

+0.

0782

+0.

0816

(0.

0301)

+0.

0785

(0.

0283)

+0.

0492

(0.

0415)

+0.

0981

(0.

0443)

1 +0.

1143

(0.

0348)

+0.

0810

(0.

0342)

+0.

1142

(0.

0350)

+0.

0810

(0.

0344)

+0.

0921

(0.

0463)

•+0.0516 (0.

0674) 1

+0.

0079

(0.

0010)

+0.

0072

(0.

0010)

+0.

0071

(0.

0010)

+0.

0079

(0.

0010)

+0.

0073

(0.

0010)

+0.

0071

(0.

0010)

+0.

0080

(0.

0013)

+0.

0062

(0.

0015)

1

i

i

i i

i .

i

I

+0.

0385

(0.

0053)

i

i

i

: ;

i i

\

0" +0.

0214

(0.

0019)

+0.

0196

(0.

0021)

+0.

0185

(0.

0022)

i i

.

i i

i i

ii

1

1 1

i i

-0.

0323

(0.

0084)

-0.

0318

-0.

0324

(0.

0079)

-0.

0315

(0.

0074)

-0.

0160

(0.

0119)

-0.

0411

(0.

0100)

1

i i

i i

i i

+0.

0566

(0.

0063)

+0.

0588

+0.

0521

(0.

0068)

+0.0488 (0.

0073)

+0.

0469

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0106)

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(0.

0110)

Const. if il il if If if if il 3

0° °S °S 0° fs ==0 fs °S 0

1 1

s.d.=

(0.0818)

1

Z

Equation

J N 0 1 - ^ i

43
Table 6-4. Calculated oontrtbutions of independent vari- ables to the autoclave expansion of neat portland cements

Table 6-5.

Independent

variable Range of variable

(percent)

Coefficients from eq 3, table 6-3

Calculated

contribution

to expansion

Calculated range of contribution to expansion

Const. -0.1146 CjA —- 1 to 15 +0. 0185 +0. 02 to +0. 28 0.26 (MgO)2 0 to 25 +0. 0071 0 to +0. 18 0. 18 Na20 -- 0 to 0.

7

_Lft HQin

-f-U. U81U U 10 T~U. UD 0. 06 K2O 0 to LO +0. 0782 0 to +0. 08 o!o8 SO3 L2to 3.6 -0. 0478 -0. 06 to -0. 17 0.11 Loss 0.3 to 3.6 +0. 0213 •+0. 01 to +0. 08 0.07 SrO 0 to 0.35 +0. 2601 0 to +0. 10 0. 10 V 0 to 0.1 +1. 086 0 to +0. 10 0.10 Cr.... 0 to 0.02 -2. 643 0 to -0. 05 0.05

"F" values for significance of reduction of variance due to added variables.

Table Equations "F" ratio D.F.

Critical

F" ratio

a=0. 01 0=0.05

6-2 0 and 1 72.44 3:175 3.38 2.68 Do 1 and 2 6.61 3:172 3.88 2.68 Do 2 and 3 6.99 4:168 3.43 2.43 Do 0 and 5 54.08 4:174 3.43 2.43 Do 5 and 6 6.39 3:171 3.88 2.68 Do 6 and 7 7.06 4:167 3.43 2.43 6-3 0 and 1 68.68 3:164 3.88 2.68 Do - 1 and 2 6.53 3:161 3.88 2.68 Do 2 and 3 6.96 4:157 3.43 2.43 Do 0 and 5 6L29 4:163 3.43 2.43 Do 6 and 6 6.17 3:160 3.88 2.68 Do 6 and 7 7.02 4:156 3.43 2.43

obtained. Another of the unknown variables was

the quantity of "free" lime in the different cements. However, the present tests confirmed that C3A and

MgO are both significantly related to the small

expansion values obtained. The coef./s.d.

ratios of most of the minor constituents were not

highly significant. This may have resulted from

the masking effect of the other unknown variables.

Judging from the equations in tables 6-2 and 6-3,

and from the calculated contributions of the dif- ferent variables to the expansion as presented in

table 6-4, it would appear that the increase in total alkalies as well as the V and SrO tend to increase

the expansion whereas the increase of SO3 content

(in the rather low percentages present in these

cements) tends to cause a decrease of the autoclave

expansion values. No information was available on the effect of the "optimum" amount of SO3 or of more than the optimum which may result in ex- pansion and deterioration of concrete at normal

temperatures.

6. Summary and Conclusions

The autoclave expansion values of the cements

used in this investigation ranged from 0.50 to minus 0.05 percent. Most of the cements had an

autoclave expansion of less than 0.10 percent. Cements classified as type I and type lA accounted

for most of the higher expansion values.

Statistical analyses by the least squares method

were used to investigate the variables associated

with the small volume changes. It was confirmed

that the MgO and C3A were .the most significant

variables involved. Increase in the content of

alkalies, both sodium and potassium, as well as an increase in SrO, V, and loss on ignition were

also associated with higher autoclave expansion

values whereas an increase in the SO3 and Cr contents were associated with lower autoclave expansion values. Lack of information on the rate of

cooling of the different cement clinkers and of the

free lime contents of the cements may have masked

the effect of other variables.

7. References

[1] H. F. Gonnerman, William Lerch and Thomas M.

Whiteside, "Investigation of the Hydration Exjmnsion Characteristics of Portland Cements." Port- land Cement Association Research Department

Bulletin 45 (1953).

[2] Interrelations between Cement and Concrete Properties, Part 1 NBS Building Science Series No. 2. Section 1—^Materials and Techniques. Section 2—

Water Requirements of Portland Cements. Section 3—^Occurrence of Minor and Trace Elements in Portland Cement.

[31 Standard Method of Test for Autoclave Expansion of Portland Cement ASTM Designation C-151-53.

[4] Federal Specification SS-C-158c Amendment 1 ; Ce- ments, Hydraulic, Methods for 'Sampling, Inspection and Testing, May 25, 1&54.

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