BUILDING SCIENCE SERIES 35

Interrelations

Between

Cement & Concrete

Properties

PART 5
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UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Interrelations Between Cement and

Concrete Properties, Part 5

Freezing-and-Thawing Durability, Saturation,

Water Loss and Absorption, Dynamic Modulus

R. L. Blaine and H. T. Arni

Building Research Division

Institute for Applied Technology

National Bureau of Standards Washington, D.C. 20234

Building Science Series 35 Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 35, 129 pages (Nov. 1971)

CODEN: BSSNB

Issued November 1971

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (Order by SD Catalog No. 013.29/2:35), Price $1.25 Stock Number 0303-0885
This publication is dedicated to the memory of Mr. Raymond L.

Blaine, who passed away during its preparation. The death of Mr. Blaine

brings deep regret to all those associated with him on this project, as well as throughout his career at the National Bureau of Standards. Mr. Blaine was the guilding light and motivating force of this tremendous undertaking for almost twenty years. His inspiration and leadership spanned

the period from the project's inception, acquisition of the cements, testing

of the cements and concretes, analysis of the data, and publication of most

of the results. For this and for his many other accomplishments and contributions in the field of cement and concrete research, including development of the Blaine Air Permeability Fineness Meter, he will long be

remembered by colleagues throughout the world.
Abstract

The concretes described in earlier parts of this series were subjected to laboratory freezing

and thawing tests, and measurements were made of the weight loss, dynamic modulus, durability factor, and number of cycles required to reach 40 percent reduction in dynamic modulus.

Companion specimens were subjected to drying and subsequent soaking in the laboratory and

to dynamic modulus tests at various ages and moisture conditions. The effect on these properties of a large number of variables connected with chemical and physical properties of the

cements and with properties of the concretes was studied by multivariable regression techniques. Air content of the concretes and degree of saturation generally had the greatest effect on the measurements. In general, minor constituents and trace elements did not show significant relationships with the measured properties, but there was evidence that some of the

variables, such as alkali content, water cement ratio, slump, and possibly setting time might

have influenced durability through an effect on the air-void system. Specimens stored in the

fog room after the freezing-and-thawing tests generally regained most or all of their original

dynamic modulus. There were significant differences between cements with respect to regain

of dynamic modulus (autogenous healing), with the non-air-entraining cements gaining more

than the air-entraining cements, on the average.

Key words : Absorption ; autogenous healing ; durability factor ; dynamic modulus of elasticity

;

saturation coefficient.

Library of Congress Catalog Card Number : 64-60095
Contents

Page Section 11. Freezing and thawing durability of concrete 1 R. L. Blaine and H. T. Arni

Section 12. Water loss and absorption of concrete 41

R. L. Blaine and H. T. Arni

Section 13. Dynamic Young's modulus of elasticity of concretes 69

R. L. Blaine and H. T. Arni
Section 11. Freezing and Thawing Durability of Concrete

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

The concretes described in earlier parts of this series were subjected to laboratory freezing

and thawing tests, and measurements were made of the weight loss, dynamic modulus, durability factor, and number of cycles required to reach 40 percent reduction in dynamic modulus.

The degree of saturation achieved during soaking before freezing and thawing was also measured. The results were analyzed to determine which of several variables connected with chemical

and physical properties of the cements plus variables connected with the concretes were sig- nificant as independent variables in multivariable regression analyses of these measurements. The air content of the concrete was the significant independent variable. Higher percentages

of dicalcium silicate (C2S), K2O, and MgO were associated with a lower durability factor. An

increase in tricalcium aluminate (C3A) and tetracalcium aluminoferrite (C4AF) were associated with greater weight loss at 40 percent reduction in dynamic modulus. There was evidence that some of the variables, such as alkali content, water-cement ratio, slump, and possibly setting

time, might have influenced durability through an effect on the air-void system. Specimens

stored in the fog room after the freezing-and-thawing tests generally regained most or all of their original dynamic modulus, with the non-air-entrained concretes generally gaining more

than the air-entrained concretes. There were also significant differences between cements in the amount of autogenous healing.

Key words: Autogenous healing; durability factor; freezing-and-thawing tests; modulus

regain; portland cement; saturation ratio; trace elements; weight loss in freezing-and-thawing

tests.

Contents

Page

1. Introduction 1 2. Materials 2

2.1. Cements 2

2.2. Aggregates 2

3. Methods of test 2

3.1. Preparation of concretes 2

3.2. Test specimens 2

3.3. Storage of specimens 3

3.4. Freezing and thawing cycles 3

3.5. Durability factor 3

3.6. Saturation ratio 3

3.7. Recovery of dynamic modulus after freezing

and thawing tests 3

4. Abbreviations . 4

5. Statistical analyses 4

6. Results of tests 5

6.1. Durability factor 5

6.1.1. Durability factor of Series 0 concretes 5

6.1.2. Durability factor of Series A concretes 8

6.2. Weight loss at 40 percent reduction of dynamic modulus 8

Page

6.2.1. Weight loss of Series 0 concretes 8

6.2.2. Weight loss of Series A concretes 9

6.3. Saturation ratio 17

6.3.1. Saturation ratio of Series 0 concretes 17

6.3.2. Saturation ratio of Series A concretes 20

6.4. Cycles of freezing and thawing 21

6.5. Autogenous healing 21

7. Discussion 26

7.1. Durability 26

7.2. Effect of alkalis on durability 28

7.3. Saturation ratio 33

7.4. Water-cement ratio 33

7.5. Slump 33

7.6. Setting time 34

7.7. Air content of test mortars versus air content

of concretes 35

8. Summary and conclusions 37

9. References 38

1. Introduction

It has been well established in both laboratory

and field tests that concrete made with air-entraining cements, or with hydraulic cements with air- entraining agents added at the time of mixing

have, among other properties, greater resistance to damage by freezing and thawing than concretes

•Present address: Federal Highway Administration, Washington, D.C.

20590.

• Figures in brackets refer to literature references at the end of this section (p. 38).

made without air-entraining agents. Bogue [1]^ reported that "no consistent relation was found

between the composition and fineness of the ce- ments and the behavior of concrete exposed to freezing and thawing." This statement was based on reports on the Portland Cement Association

Long-Time Study on Cement Performance in

Concrete [2]. Grieb and Werner [3] in their further study of concretes made of the cements used in the Long1
Time Study concluded that "concrete prepared

with cements having tricalcium aluminate (C3A)

content of more than 10 percent had poorer durabihty than concrete made with cements having

C3A contents of less than 10 percent." Mather [4] reported on freeze-thaw tests on concretes made

of the same cements but with an air-entraining

agent added and found all highly resistant to damage by freezing and thawing. Oleson and

Verbeck [5] found "no evidence of a significant

effect of cement composition or fineness, per se, on concrete performance" (when concrete speci- mens made of these cements were stored outdoors

at the Illinois Test Plot for more than 25 years).

Laboratory tests for evaluation of resistance to

freezing and thawing are normally made with

specimens which have not been permitted to dry

[6], whereas concretes in structures usually (but

not always) have a period when some of the water

evaporates before being subjected to freezing. In

concretes that have not been permitted to dry,

the size and spacing of small bubbles of entrained

air have been shown to be of paramount importance [7.] Concrete specimens that have been

allowed to air-dry take some time to become

saturated to the extent that they are damaged by

the freezing of the water in the concrete. Various criteria have been used to evaluate the

effects of freezing and thawing on concrete. Among

these are loss of compressive or flexural strength.

loss of weight, and expansion of the concrete re- sulting from repeated freezing and thawing.

Hornibrook [8] found that when specimens were

left in the thawing water for several days after a

freezing-and-thawing cycle, an increase in resonant

frequency occurred which was attributed to autog- enous healing. Such autogenous healing of concrete partially damaged by freezing has not been

fully explored. Present test methods [6] require

that concrete specimens be kept in a frozen condition when the sequence of freezing and thawing

cycles is interrupted.

The present investigation was undertaken to determine whether the chemical composition of

the cements was associated directly or indirectly

with the durability factor calculated from freezingand-thawing tests or with weight loss of concrete

which had been partially air dried and then re- soaked prior to freezing. In view of the fact that

the degree of saturation of the concrete plays such

and important role in the results of freezing-andthawing tests, studies were made of the factors

associated with a calculated saturation ratio of the

concretes. Studies were also made to determine

the extent of recovery of the dynamic modulus of concretes (autogenous healing) after the freezingand-thawing tests had been completed. Because

of the limited quantities of the various cements

available it was not possible to make additional

tests with air-entraining agents added.

2. Materials

2.1. Cements

The cements used in this investigation have

previously been described. The frequency distri- butions of the results of chemical analyses as well as spectrochemical analyses were reported in part

1, sections 2 and 3, of this series of articles [9], and

other tests with these cements have been reported

in parts 2, 3, and 4 [10, 11, 12]. Most of the 199

commercial portland cements were obtained from

different areas of the United States, but a few came from other countries. The cements were

classified as to type on the basis of chemical and

physical properties. ^

2.2. Aggregates

The coarse and fine aggregates are described in part 1, section 1 [9] of this series of papers. A high

quality, 1-in maximum size, rounded, quartzite, coarse aggregate (White Marsh) and a sand from

the same source were used for making the concretes. The fineness modulus of the sand was 2.82,

of the coarse aggregates 6.82, and of the combined

aggregates 4.82.

3. Methods of Test

3.1. Preparation of Concretes

The details of the proportioning and mixing of

the concretes were described in part 1, section 1, of this series of articles [9]. Two series of concretes were made with these

cements. One series (Series 0) was made with a

constant water/cement ratio of 0.635. A second

series (Series A) was made in which the water

content was changed, if necessary, to obtain a

concrete with a 5 + 1-in slump. In the two series,

2 On the basis of this classification, there were 82 Type I, 8 Type lA, 68 Type II, 3 Type IIA, 20 Type III, 3 Type IV, and 12 Type V cements.

the cement-to-aggregate ratio was the same. The

cement factor varied to some extent from the

nominal 5J^ bags of cement per cubic yard, primarily because of variations of the entrained and

entrapped air.

3.2. Test Specimens

Eight 3- X 4- X 16-in specimens were made

from each of the cements, four in each of the two

series of concretes. These were made from the same batches of concrete as those used for the

6- X 8- X 16-in specimens used for shrinkage and

2
expansion tests [12]. The specimens were cast in

steel molds in accordance with ASTM Designation

C 192-52T procedures [13] except that the molds

were lined with sheet plastic and no oil or grease was used. Two of the 3- by 4- by 16-in specimens

were subjected to laboratory freezing-and-thawing

tests, and the other two were placed in the field for natural weathering tests.

3.3. Storage of Specimens

The 3- X 4- X 16-in concrete specimens were

covered with moist burlap for the first 20 to 24

hours, then removed from the molds and placed

in a fog room at 100-percent relative humidity

(RH). At the age of 14 days, the specimens were removed from the fog room and stored on end in laboratory air at 73 °F and 50-percent relative

humidity for 4 weeks. After this drying period,

the two specimens from each batch which were to be subjected to laboratory freezing-and-thawing

tests were placed in water at 40 °F. After 24 hours

soaking the freezing-and-thawing tests were

started. The weight, fundamental resonant fre- quencies, and dynamic Young's modulus of elasticity (dynamic E) were determined at 1 and 14

days, at the time just prior to placing in the 40 °F

water, at the start of the freezing cycle, and at

periodic intervals during the freezing-and-thawing

tests. The fundamental transverse resonant fre- quencies were determined in accordance with

ASTM Designation C 215 [14]. After completion

of the freezing-and-thawing tests the specimens were placed in the fog room at 100-percent RH,

and resonant frequency measurements were again

made after storage periods ranging from approximately one to five years.

3.4. Freezing-and-Thawing Cycles

The two duplicate concrete specimens from each

concrete batch were frozen in water at 0 °F and

thawed in water at 40 °F with each cycle completed in two hours in accordance with ASTM

Designation C 290 [15]. The freezing and thawing

tests were continued until there was a 40 percent

reduction in dynamic modulus.

The calculations of dynamic Young's modulus

of elasticity took into account the weights of the

specimens and the fundamental resonant frequencies, but no corrections were made for possible

variations of Poisson's ratio nor for dimensional

changes caused by sloughing of the specimens. In

other words, instead of the ratio of the squares of the resonant frequencies being used as suggested

in C 290, the following formula was used for

relative dynamic modulus:

where Pc = relative dynamic modulus of elasticity, percent, after c cycles of freez- ing and thawing W = weight at 0 cycles of freezing and

thawing

VFi = weight after c cycles of freezing and

thawing n = resonant frequency at 0 cycles of freezing and thawing, and

tlx — resonant frequency after c cycles of freezing and thawing.

3.5. Durability Factor

Durability factors (DF) were calculated using

the formula given in ASTM Designation C 290

based on a termination of the tests at 300 cycles

of freezing and thawing or 60 percent relative

dynamic modulus. In many instances, with the

concretes made with air-entraining cements, the

freezing-and-thawing tests were continued past

300 cycles in order to obtain the 40 percent reduction in dynamic modulus. The values for the two

duplicate specimens from each series were aver- aged.

3.6. Saturation Ratio

The saturation ratio was calculated from the

weight lost during 28 days drying in laboratory

air, the weight gained during 24 hours soaking at 40 °F (prior to freezing and thawing), and the

volume of air measured in the plastic concrete. The weight lost during drying and the weight

gained during soaking, in grams, were taken as the water gained and lost in ml. The percentage

of air, determined gravimetrically in the plastic

concrete, multiplied by the volume of the speci- mens in ml was taken as the volume of air in the

plastic concrete. The measured volume of air plus

the volume of water lost during drying was taken

as the total volume of air voids in the hardened

concrete available to take up water. The ratio of the volume of water gained during soaking to the

total volume of air voids is the saturation ratio. These values were considered as the degree of saturation at the start of the freezing-and-thawing

tests. The ratios ranged from about 0.4 to 0.8 for non-air-entrained concrete and 0.2 to 0.4 for air- entrained concretes.

3.7. Recovery of Dynamic Modulus After Freezing-and-Thawing Tests

Autogenous healing of the concrete specimens

after freezing-and-thawing tests was evaluated by

studying the ratio of dynamic modulus after various periods of moist storage following the

freezing-and-thawing tests.

3
4. Abbreviations

The abbreviations, notations, etc., used in this

section for chemical and physical properties of the

cements are the same as those used in previous

sections of this series of articles.^ In this section, the prefix "0" of the four-letter

titles for the various dependent variables refers to the concretes of Series 0 in which a water/cement

ratio (w/c) of 0.635 was used. The prefix "A"

refers to the second series of concretes in which

the water was readjusted, if necessary, to give a

5 + 1-in slump. The abbreviations for the dependent variables used in this section are as

follows:

For Series 0 concretes made with a w/c of 0.635

ODUR = durability factor of concrete speci- mens which had been air-dried

then subjected to rapid freezing

and thawing in water.

OWTL = weight loss of concrete specimens at the time of 40 percent loss of dynamic modulus expressed as per- cent of weight at 0 cycles of

freezing and thawing.

OSAT = ratio of volume of water absorbed in

24 hours (prior to start of freezing

test) to possible absorption.

OAIR = air content in percent by volume

OCYS = number of freezing-and-thawing cycles required to cause a 40 percent

reduction in dynamic modulus.

For Series A concretes having a 5 ± 1-in slump,

the letter "A" is used instead of "0" as ADUR,

AWTL, ASAT, AAIR, and ACYS for the differ- ent variables.

5. Statistical Analyses

The statistical techniques used to find and

evaluate the independent variables associated

with the durability factor, weight loss, saturation,

and dynamic modulus ratios have been described

in a previous section of this series entitled "Materials and Techniques" [9]. The statistical treat- ment was the same as that used in all previous

sections of this series of articles. Multiple regres- sion equations were calculated by the method of least squares using various independent variables.

As in previous sections, equations were calculated

for both AE + NAE cements and NAE cements.

Comparisons were made using only commonly

determined variables and also using these to- gether with minor and trace elements.

Ratios of reduction in variance to original vari- ance ("F" ratios) obtained by fitting equations were calculated for two kinds of cases: (1) for equations including one or a few main independent

variables as compared to the original data on the

dependent variable, or (2) for equations in which

additional independent variables were included as compared to a previous equation with fewer

variables^ The "F" ratios and critical "F" values

which, when equalled or exceeded, indicate sig-

' These abbreviations include the use of C3A, CaS, C2S and C4AF for the

calciJated potential compounds, tricalcium aluminate, tricalcium silicate, dicalcium silicate, and tetracalcium aluminoferrite, respectively. Insol for insoluble residue. Loss for loss on ignition, APF for air permeability fine- ness, and Wagn for Wagner turbidimeter fineness are also used. AE +

NAE refers to airtentraining plus non-air-entraining cements, and NAE

to the non-air-entraining cements.

' Statistical terms and notations employed in this section are the same

as those used in previous sections of this series of articles. For example,

S.D. refers to the estimated standard deviation 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 estimated standard deviation of a coefficient of an independent variable used in a

fitted equation. The term coef./s.d. is the ratio of the estimated coefficient

(of an independent variable used in an equation) to its estimated standard

deviation. "DF" designates degrees of freedom. As indicated in previous

sections, a coef./s.d. ratio greater than 1.0 was considered to be of sufficient significance to warrant further investigation.

nificance at the a = 0.05 and a = 0.01 levels are summarized in table 11-27.

After it had been determined which independent

variables were significantly associated with the

dependent variable when used in an equation, the

residuals of the equation were fitted by the method

of least squares to other single independent variables and the reduction in variance calculated. If any of the additional independent variables indicated a significant reduction in variance, they were tried in the equation and retained if the

coef./s.d. ratio was greater than 1.0. Equations were also computed for the "odds"

and "evens" in the array of cements. Comparisons

were made of the coefficients of the variables in the two groups of cements, and these were compared to the coefficients and coef./s.d. ratios

computed for all the cements.

Although freezing-and-thawing tests were made

on all 199 cements, the calculations of the equations presented in this article were limited to those

for which trace elements had been determined.

Equations presented in this article were selected

from a large number of trial equations indicating

the calculated relationship of various independent

variables to durability and degree of saturation.

These equations were selected primarily to indi- cate the association with dependent variables of commonly determined variables having coef./s.d.

ratios greater than 1.0 when used in multivariable

equations, and also to indicate which of the minor

and trace elements might have had an effect. Some of the limitations on interpretations of

multivariable regression equations have been dis- cussed in part 1, section 1, subsections 4.2, 4.3,

and 5 [9]. Other limitations and problems of interpretation have also been discussed in other sec- tions of this series of articles.

4
Table 11-1. Frequency distribution of cements with respect to durability factor of concretes having a nominal 5)4. bags cement

-per cubic yard and a water-cement ratio of 0.635 (ODUR)

Durability factor

0 10 20 30 40 50 60 70 80 90

to to to to to to to to to to Total

10 20 30 40 50 60 70 80 90 100

Number of cements

I.- 10 23 28 16 3 2 82868

320

315

IA 1 4 2 1 II 12 22 25 5 2 2 IIA 3

III 4 5 4 3 2 2 IIIA 3 IV, V 4 8 3 Total 30 58 60 24 7 6 1 4 8 1 199

6. Results of Tests

6.1. Durability Factor

6.1.1. Durability Factor of Series O Concretes The frequency distribution of the durability

factors of concretes made with a water-cement

ratio of 0.635 (ODUR) is presented in table 11-1.

The concretes made with air-entraining cements

Types lA, IIA, and IIIA all had higher durabilityfactor values than did those made with the nonair-entraining cements. There was a fairly broad

distribution of values and there was an overlapping of the values of the concretes made with

different types of NAE cements. Eighty percent

of the non-air-entrained concretes had durability

factors below 30, while all of the air-entrained concretes had durability factors greater than 60. Equations selected from those computed to determine the various independent variables asso- ciated with the durability factor are presented in table 11-2. The use of the air content in eq 1, or the saturation coefficient at the start of the

freezing-and-thawing tests (OSAT) in eq 2, as independent variables each resulted in a highly

significant reduction in variance. (See table 11-27).

With the use of the air content and the additional use in equation 3 of C3S, C2S, NaoO, K2O, MgO

and fineness, all commonly determined independent variables, there was a significant reduction in variance. Of the trace elements, Ba, Rb, Pb, Ti,

and Cu had coef./s.d. ratios greater than 1.0 when

used with commonly determined independent

variables in the multivariable regression equation

as indicated in eq 4. Use of the trace elements in the equation resulted in a highly significant re- duction in variance. (See table 11-27). In eqs 4A

and 4B, calculated for the "odds" and "evens" in the array of cements, Pb and Cu, as well as C3S

and fineness had coef./s.d. ratios less than 1.0 in one or the other of the smaller groups of cements^

' As has been indicated in previous sections, chance occurrence of two

or more extreme values in one of the two groups may cause such anomalous

results. Another possible contributing factor was the assignment of zero to values for trace elements having less than the lowest reported value.

Equations 5 and 6, calculated using SiOa instead

of C3S and C2S, also resulted in a reduction in

variance significant at the 1.0 percent level. The

use of the trace elements in addition to the com- monly determined variables in eq 6 resulted in a

significant reduction in variance. (See table 11-27). In the equations for the "odds" and "evens" (eqs

6A and 6B) fineness, Ba, and Pb had coef./s.d.

ratios less than 1.0 in one or the other of the

smaller groups of cements.

Equations calculated for the NAE cements are presented in table 11-3. The coefficients for the

air content and saturation coefficient in eqs 1 and

2 respectively were highly significant, but the

coef./s.d. ratios were lower than when the AE

cements were included as in table 11-2. The coefficients for the other independent variables in eqs

3, 4, 5, and 6 of table 11-3 are in reasonable agree- ment with those of the previous table. Using

commonly determined variables in eqs 3 and 5

resulted in highly significant reductions in vari- ance, and the use of trace elements in eqs 4 and 6

each resulted in highly significant reductions in variance as a result of the added independent

variables. It may noted, however, that in equations for the "odds" and "evens" eqs 4A, 4B, 6A,

and 6B, C3S, Na20, fineness, Ba, and Pb had

coef./s.d. ratios less than 1.0 in one or the other

of the equations for the smaller groups of cements.

The estimated contributions and ranges of contributions to the durability factor of the various

independent variables calculated from the coefficients of eq 4 table 11-3 are presented in table

11-4. The ranges of the independent variables were assumed to be the same as for all 199 cements

previously described in sections 2 and 3 of this

series [9]. An increase in air content of the NAE

cements resulted in an increase in the durability

factor. Increase in C3S, K2O, MgO, fineness, Rb,

Ti, and Cu was associated with a decrease in the

durability factor. The coefficients of C3S, NaoO,

Ba and Pb were of doubtful significance as the

coef./s.d. ratios were less than 2.0.

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Table 11-4. Calculated contributions of independent variables

to the durability factor of concretes having a nominal 5 Yi bags cement per cubic yard and a water cement ratio of 0.635 (ODUR)

Calculated Independent Ranges of Coefficients Calculated range of variables variables. from eq 4 contributions contribu-

(percent) table 11-4 to UDUK tions to ODUR

Const. = +94

Air content NAE cements 0 to 4.5 +6.830 0 to +31 31 CsS 20 to 65 -0.5456 -11 to -35 24 C2S 5 to 50 —0.8319 -4 to -42 38

"KT n ^* * JNa2U^^ 0 to 0.7 — 7.094 0 to —

5

5 K2O 0 to 1.1 -19.34 0 to -21 21 MgO 0 to 5 -2.866 0 to -14 14 APF *2500 to 5500 -0.00346 -9 to -19 10 Ba** 0 to 0.2 -37.03 0 to -7 7 Rb 0 to 0.01 -883 0 to -8 8 Pb** 0 to 0.05 -190.6 0 to -10 10

Ti 0 to 1.0 -14.72 Oto -15 15 Cu 0 to 0.05 -176.9 0 to -8 8

* cmVg.

** Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

Somewhat different values may be obtained by

use of other equations presented in table 11-3 for NAE cements and also by use of equations in table 11-2 for AE -|- NAE cements. Other tables

of the estimated contributions are, for the sake

of consistency, presented for the NAE cements.

In all instances, an equation having potential

compounds and all other independent variables

having coef./s.d. ratios greater than 1.0 will be

used. In subsection 7, a summary table is also

presented of equations for the AE -|- NAE

cements.

6.1.2. Durability Factor of Series A Concretes

The frequency distribution of the durability

factors of concretes made with sufficient water for a 5 + 1-in slump (ADUR) is presented in table

11-5. All but two of the 14 concretes made with

the air-entraining cements had durability factors

higher than those for concretes made with any of the non-air-entrained cements and 78 percent of

the non-air-entrained concretes had durability

factors below 30. There was an overlapping of the

durability values of the NAE concretes made with

the different types and a broad distribution of

results. The equations relating the durability factor of AE -|- NAE cements to the independent variables are presented in table 11-6. Equations 1 and 2

indicate the relationships of the air content and

the saturation ratio (ASAT) respectively to the

durability factor. The coefficients of both independent variables were highly significant, and in both equations there were highly significant re- ductions in variance. (See table 11-27).

The use of air content together with other

commonly determined variables C3S, K2O, MgO,

and APF in eq 3 resulted in a further significant

reduction in variance, and the additional use of the trace elements Ba, Rb, Pb, Ti, and Cu in eq 4

resulted in a further reduction in variance, significant at the 1.0 percent level. (See table 11-27,

p. 00.) C3S and Na20 had coef./s.d. ratios less than 1.0 when included with the other variables

with the 5 + 1-in slump concretes but greater

than 1.0 in the equations in table 11-2 for the

0.635 w/c concretes. The use of the oxides CaO and Si02 as independent variables (eq 5) together with other com- monly determined variables, K2O, MgO, and

fineness, resulted in an S.D. value comparable with

that of eq 3 where C2S was used, and a highly

significant reduction in variance was obtained.

(See table 11-27.) The fineness of the cements had

a coef./s.d. ratio less than 1.0 when included with

the other variables in eq 5 but between 1.0 and

2.0 in eq 6. When fineness was used as an independent variable together with the trace elements

and other commonly determined variables (eq 6), there was a reduction in variance significant at the

1.0-percent level although the coefficients of none

of the added independent variables were, individually, highly significant.

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

4A, 4B, 6A, and 6B, there were instances where

CaO, MgO, fineness, Ba, Pb, Ti, and Cu had

coef./s.d. ratios less than 1.0. The equations presented in table 11-7 indicate

the independent variables associated with the

durability factor for concretes having a 5 + 1-in

slump and made from NAE cements. The same

independent variables had coef./s.d. ratios greater

than 1.0 as in table 11-6 where the AE cements

were included. The use of commonly determined

variables (eqs 3 and 5) resulted in highly significant reductions in variance, and with the use of

the trace elements and fineness in eqs 4 and 6, a

further reduction in variance was obtained (See

table 11-27.) In equations for the "odds" and

"evens," eqs 4A, 4B, 6A, and 6B, there were in- stances where CaO, fineness, and all of the trace elements had coef./s.d. ratios less than 1.0 in ones or the other of the smaller groups of cements.

The estimated contributions and ranges of the

contributions to the durability factor of concretes having a 5 + 1-in slump calculated from the coefficients of eq 4, table 11-7 are presented in table

11-8. Increased air content was associated with

increased durability. Increases in C2S, K2O, MgO,

and possibly fineness, Ti, and Cu were associated

with lower durability factor values.

6.2. Weight Loss at 40 Percent Reduction of

Dynamic Modulus

6.2.1. Weight Loss of Series O Concretes The frequency distribution of weight loss of the

Series 0 concrete specimens (OWTL) at the time

of 40 percent reduction of dynamic modulus in the freezing-and-thawing test is presented in table

11-9. These concrete specimens were made using a water-cement ratio of 0.635. There was actually a slight weight gain with 11 of the concretes and

8
Table 11-5. Frequency distribution of cements with respect to durability factor of concretes having a nominal SYi bags cement

per cubic yard and a slump of 5 ± 1 inches (ADUR)

Durability factor

0 10 20 30 40 50 60 70 80 Type cement to to to to to to to to to Total

10 20 30 40 50 60 70 80 90

Number of cements

I 8 27 22 15 4 2

2

1

1 79

867

320

315

lA 3 3

II 12 19 26 7 1 1 IIA 1 2 III 3 4 6 2 3 1 1 IIIA 3 IV, V 4 7 2 2 Total 27 57 56 26 8 6 3 4 8 195

a loss of up to 20 to 22 percent with other

concretes. The specimens which showed a weight gain were all specimens which failed very rapidly in the

freezing-and-thawing test. One-day soaking in water at 40 °F is not sufficient to saturate the

specimens, as is shown below by the saturation

ratios. Thus all the specimens showed weight gain

in the first few cycles of freezing and thawing as the process of freezing in water forced water into

unfilled pores of the concrete. Then weight losses occurred as the surface sloughed off with continued freezing-and-thawing cycles. The only

specimens which showed a weight gain, consequently, were those that failed in the first few

cycles while they were still taking up water and

before sloughing had started.

The concretes made with the AE cements had

weight-loss values above the mean for all cements.

There was an overlapping of the values of the

different types of cements.

The equations for AE and NAE cements re- lating weight loss of the concrete specimens at the time of 40 percent reduction of dynamic

modulus to various independent variables are presented in table 11-10. Equation 1 indicates

that increased air content was associated with

increased weight loss. The use of other commonly

determined variables C3A, C4AF, Na20, and K2O

(in addition to the air content) (eq 2) resulted in a significant reduction in variance. With the additional use of the trace elements Rb, Pb, Ti, and

Zr (eq 3) a further reduction in variance significant at the 1.0 percent level was attained. (See

table 11-27.) In equations 3A and 3B calculated

for the "odds" and "evens" in the array of ce- ments, Rb, Ti, and Zr had coef./s.d. ratios less than 1.0 in one or the other of the smaller groups.

The use of AI2O3, Fe^Oz, SO3 and AI2O3/SO3

(eq 4) instead of C3A and C4AF as in eq 2, together

with Na20 and K2O, the other commonly determined independent variables, also resulted in a

significant reduction in S.D. value. (See table

11-27.) By using the trace elements Rb, Pb, Ti,

Zr, and Cr in eq 5, a further significant reduction

in variance was obtained. Each of these trace

, elements, as well as AI2O3, SO3, and the AI2O3/SO

ratio had coef./s.d. ratios less than 1.0 in one or the other of the equations for the "odds" and

"evens" (eqs 5A and 5B).

Table 11-11 shows a series of equations for the

weight loss at the time of 40 percent reduction of

dynamic modulus of NAE cements. As indicated

in eq 1, the coef./s.d. ratio of the air content was

less than 1.0. When used with other commonly

determined independent variables (eqs 2 and 4)

the coef./s.d. ratio was greater than 3.0. The use

of the commonly determined variables (eqs 2 and

4) resulted in highly significant reductions in vari- ance. The additional use of trace elements Rb,

Pb, Ti, and Zr (eq 3), or these together with Cr

(eq 5) resulted in reductions in variance significant at the 1.0 percent level (See table 11-27). In eqs

3A, 3B, 5A, and 5B calculated for the "odds" and

"evens," Rb, Zr, and Cr as well as AI2O3, SO3, and

AI2O3/SO3 had coef./s.d. ratios less than 1.0 in one or the other or both of the equations calculated for the smaller groups.

Estimated contributions and ranges of contributions to the percentage weight loss of concretes made with NAE cements at the time of 40 percent

reduction of dynamic modulus as calculated from

the coefficients of eq 3, table 11-11, are presented

in table 11-12. Increases in air content, C3A, and

C4AF were associated with an increase in the

weight loss. Increases in K2O and possibly Na20,

Rb, Pb, and Ti were associated with a decrease in the weight loss.

6.2.2. Weight Loss of Series A Concretes The frequency distribution of the weight loss of Series A concrete specimens (AW^TL) at the

time of 40 percent reduction of dynamic modulus

in the freezing-and-thawing tests is presented in table 11-13. These concretes were made with sufficient water to produce a 5 + 1-in slump. The

specimens made with the air-entraining cements

all had weight-loss values above the average for

all specimens, but there was some overlapping

with the concretes made with NAE cements.

There was an overlapping of the groups of values

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11
Table 11-8. Calculated contributions of independent variables

to the durability factor of concretes having a nominal 5 Yi bags cement per cubic yard and a slump of 5 ± 1 inch (ADUR)

Calculatec Independent Range of Coefficients Calculated range of variables variable from eq 4 Contributions contribu-

(percent) table 11-7 to ADUR tion to ADUR

Const. = +54

Air content NAE cements

0 to 5.0 +6.539 0 to +33 33

Q 4106 2 to 21 19 KsO 0 to 1.1 -16.03 0 to -18 18 MgO 0 to 5.0 -2.47 0 to -12 12 APF *2500 to 5500 -0.00337 -8 to -19 11 Ba** 0 to 0.2 -43.6 0 to -9 9 Rb** 0 to 0.01 -675.9 0 to -7 7 Pb** 0 to 0.05 -184.4 0 to -9 9 Ti 0 to 1.0 -13.56 0 to -14 14 Cu 0 to 0.05 -218.1 0 to -11 11

* CmVg.

** Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

for the different types of NAE cements. As indicated in table 11-13, a few cements showed the

slight weight gain characteristic of specimens

which failed in the first few cycles.

The series of equations presented in table 11-14

indicates the association of various independent

variables to the percentage weight loss (AWTL)

at the time of 40 percent reduction in dynamic

modulus of specimens made of Series A concretes. Equation 1 indicates that an increase in the

water/cement ratio is associated at the 5.0 percent

significance level with a decrease in the weight

loss. (See table 11-27.) Equation 2 indicates the

relationship of the air content of the concrete to the weight loss. The reduction in variance is greater than for eq 1. The additional use of other

commonly determined variables C3A, C4AF, Na20,

and K2O in eq 3, or AI2O3, Fe203, Na20, and K2O

in eq 5, caused a reduction in variance, significant at the 1.0 percent level. The additional use of the

Table 11-9. Frequency distribution of cements with respect to percentage weight loss of concrete specimens at the time of iO percent

loss of dynamic modulus in the freeze-thaw test. The specimens were made of concretes having a nominal 5 Yi bags cement per

cubic yard and a water-cement ratio of 0.635 (OWTL)

Percentage weight loss

-2 0 2 4 6 8 10 12 14 16 18 20 Type cement to to to to to to to to to to to to Total

0 2 4 6 8 10 12 14 16 18 20 22

Number of cements

I 5 17 12 16 8 12

1 12

6 4

3

5

2

1 82

8 68

320

315

lA 3

II 2 13 5 14 9 7 1 IIA 2 1 III 3 3 3 3 2 3 12

1

1 1 IIIA 1 IV, v 1 4 1 2 3 3 Total 11 37 21 35 22 31 17 13 6 4 1 1 199

12,
S.D. 3.968 3.352 3.177 2.880 3.339 3.345 3.168 2.890 3.305

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(58.49)

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(71.94)

-81.83

(96.80)

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I "

in 00 to in c^j oocM to in ooo

iH to 1-t in OS

t>os

t- TP TP tree CM 1-4 t-(O 00 Tf 1-1 in CO o

CM CO

00 to TPCO

to TP ^co

osTf oin

toco l> Tf d f-J d

in Tj« in OS

CM O

<#oo coin oco mt00 i-H C- iH o o oo oo

05 N oo

"^O 1-H oo oo oo

(M in inc^

in rH dci

OCO

l> 00 TP CO

1-J d O N O

t- in

.- d

th in 00 o o

-"J" 00 «D t- rH

in CO <7s CO ^ in »4d wd

00 o 'I

(N IN

HO oi

0<D

f-i O m

too

00 in TfCO

E-i O T,

(D in t- in

II II II II

H iH T-l IN W ^ N

inc^

I ^

CO in oco

in Tj» 00 CO

I

o

T

tOOsl ooCO 00

Ol in

^* d

in

•o ren) •oo

OWTL

s.d.

OWTL

s.d.

OWTL

s.d.

OWTL

s.d.

13
Table 11-12. Calculated contributions of independent vari- ables to the percentage weight loss in the freeze-thaw durability

test at the time of UO percent reduction of dynamic modulus

of concretes of nominal 5 Vi bags cement per cubic yard and

a water cement ratio of 0.635 (OWTL)

Independent

variables Range of variable

(percent)

Coefficients from eq. 3 table 11-11

Calculated

contributions

to OWTL

Calculated range of contribution to OWTL

Const. = -2.1

Air content NAE cements. 0 to 4.5 +1.881 0 to +8.5 8.5 CsA 1 to 15 +0.4462 +0.4 to 6.7 6.3 CiAF 1 to 16 +0.8041 +0.8 to +12.9 12.1 Na20 0 to 0.7 -4.168 0 to -2.9 2.9 K2O 0 to 1.1 -8.96 0 to -9.9 9.9 Rb 0 to 0.01 -344.4 0 to -3.4 3.4 Pb 0 to 0.05 -88.71 0 to -4.5 4.5 Ti 0 to 1.0 -7.28 0 to -7.3 7.3 Zr** 0 to 0.5 +12.34 0 to +6.2 6.2

** Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

trace elements, Mn, Rb, Pb, and Ti (eqs 4 and 6)

resulted in a further reduction in variance (see

table 11-27) although the coefficients for the individual trace elements were not highly significant.

In equations calculated for the "odds" and

"evens," eqs 4A, 4B, 6A, and 6B, the coef./s.d.

ratios for Fe^Os, Na20, Pb, and Ti were less than

1.0 in one or the other of the equations calculated

for the smaller groups of cements.

An analogous series of equations for the NAE

cements is presented in table 11-15. The coef./s.d.

ratios of w/c and air content (eqs 1 and 2) were

both less than 1.0. When these were used with

other commonly determined variables (eqs 3 and

5), the coefficient for air content was probably

significant, and the reduction in variance as a

result of the added variables was highly signifi- cant. The additional use of four trace elements

(eqs 4 and 6) caused a further reduction in variTable 11-13. Frequency distribution of cements with respect to percentage weight loss of concrete specimens at the time of UO percent

loss of dynamic modulus in the freeze-thaw test. The specimens were made of concretes having a nominal 5 Yi bags cement per

cubic yard and a slump of 5 ± 1 inches {AWTL)

Percentage weight loss

-2 0 2 4 6 8 10 12 14 16 18 20 Type cement to to to to to to to to to to to or Total

0 2 4 6 8 10 12 14 16 18 20 more

Number of cements

I 4 16 11 9 11 14

1 11

9 2

36

2

11

1

2

3

1

1 79

867

320

315

ia 1 II 3 10 9 10 11 5

132

1

1 iia

III 2 1 5 2 3 2 1 IIIA

IV, V. 1 5 1 2 2 2 Total 10 32 26 23 27 30 21 16 6 1 1 2 195

14
•I

eOl-H

I ^ oeo

00 eo

00 (M cnoo

I ^

©CO

00

O) 00

I ^

t- 00

00 eo

I

00

1/5 OS

CO o

CO CO

r-t OS rH Ol t-^ (N eo oi

I ^ I -

00 Ol

1-1 c- o i> in cc Oi-( OS o

OS r-J OS t>

''t N cooi

t- 00 o tOiH 04r-l

I

CD ^ t- 00 moo W3C0 t> t- iftiH COOO

CD 00 CJ CO IrtOO CD O f- 00 COCO CD 00 CD O

OS iom toco 00 o OS m m lo ^dco coo

»Hi-I 04 oicJ tHCg* "Hi-I OJrH ojoi rHN ,w ,w ,^ |_ 1^ 1^

COrH

Oit> l>CO do

oco

COOO

CD

OS CO d d

CD CD COOO

OS lO

T-i d

U5 -^l* O CO d d

t-id

cow

ooo ^ d rH d

CJCO

•H d

dd

oco dd

COM

CO w

d d

t> CO M 00

CO w

d d

t> O

d d

t-00

IN O OO

CJl 00

CO CO

CO d d +-'

00

in w

d d

OS CO

CO »H d d

o t- O W

d d

OCO dd 0()(N d d

TfO

OON

OS CO

00 w

d d

O OJ

CO

C^o«o

OlrH d d

OSinco 00^

OON d d

CO o CO C<1 CO

CO ac +

in o +

t-os

OS CO

OS OS

t-CO

in lO rHOS O lO

OS o

oeo

»-i 1-1 y~t in +^

II II

OON

OSOJ o in r^OS

Oi-< 1-1^

II II II II

coos

n<co o q

coco

I ~

n

<

< oi

HZ

ren) T3Oo

AWTL

s.d.

AWTL 8.d.AWTL

s.d.

AWTL

s.d.

iH iH OJ

ss s

c c .2 g E .2

CD 00 ,

O O rj 2:2 *
s

as

s5^

CO wi 05 CD

CO CD

00 OS

00*00CO

iCOO

I ^

00 t-; CTS W

O N CO

rP lO CD N

CO 1-1 CON

C<1 00

t-HCO

iM CO

in T}«

1 ^

M CO COW

I ^

Ol CD O CO 0(M

CD (N

t> CD

00 CO

I ^

to t>

co t> CD (N

CO C^J

I ^

tCO

CO 1-i <M 0000

! ^

00 CO

00 t> t>00

NO iHt- COlrt 00 00 COO M t> t> »0 l> OC U5 Tj< li^ Tj< iHW OO in-^ rj< r-lTH OC

oth^ Oth Nci oooi, OrH ow^ 7 7 7 '7 7 7

'

00 00 ihP coco OSW 00 00 -^CD t- cJ" O OJ

lf5 coos -^UO OS U5 tP OS 00 U5 COW

OCO OS>0 OliO NO OCD OSlC |Wr-5 C^*|w,-1 |wN W|woi N,w»H |wr-I M r-I c^i 1^ 1^

COCO

irt o

CO t- t>co d d

00 CO

CO 00 OCO

iC o 00 iH o m

1-H d +^

1/5 U5 CJN

00d d

4-^

t- lO NO OiH iH t- NO CD O CO 00 CDOO

COCO lOCO TjJ "^co wd f-5d 1-1 d f-5d +^ +^ +^ ^---^

CD r> in iH d d

eooi

OS TP

iCCD r-l d d

1-1 CD iCN

CON dd

CO 00

CD tC- O ION d d

m TP

C- CO

OOr-l

lOi-H O O o o

iH iH NCD

iC

in w d d

to

ini-t OS CO OCO d d

in in

CO in Tpco

OS CO d d

N 00 TpN N CO

tA d

N 00 OSN

COOS tPN N CO

TP CO ooo

Tj*t- in Tp OO OO

OS OS OCO OCD

00 Tp d d

tHCO iCN

CD tTprH m TP oto

CD d O N ON

00 CO

t>

CD 7-4 dco i-HN ON

ICi-H in 00 CO o

d N N

[[ II II

(odd)

(even) (odd)

(even)

ATWL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL

s.d.

AWTL 3.d.

Note

o* d

CO < m'

in CO

6A. mCO

is s

a a S, s a .2

a) a, «

cooo >a

O O Q 2Z *

16
Table 11-16. Calculated contributions of independent vari- ables to the percentage weight loss in the freeze-thaw durability

test at the time of J^O percent reduction of dynamic modulus

of concretes of nominal 5 ]/2 bags cement per cubic yard and

a slump of 5 ± 1 inch. (AWTL)

Calculated Independent Range of Coefficients Calculated ranges of variables variable from eq 4 contributions contribu-

(percent) table 11-15 to AWTL tion to AWTL

Const. = +0.4

Air content NAE cements. 0 to 5.0 +1.244 0 to +6.2 6.2 CzA 1 to 15 +0.5875 +0.6 to +8.8 8.2 C4AF 1 to 16 +0.6593 0 to +4.6 4.6 Na20** - 0 to 0.7 -2.931 0 to -3.2 3.2 K2O 0 to 1.1 -10.51 0 to -10.5 10.5 Mn 0 to 1.0 -6.012 0 to -6.0 6.0 Rb 0 to 0.01 -340.8 0 to -3.4 3.4 Pb** 0 to 0.05 -54.97 0 to -2.7 2.7 Ti 0 to 1.0 -5.534 0 to -5.5 5.5

** Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0

ance, significant at the 1.0-percent level. (See

table 11-27.) The coef./s.d. ratio of air content in eqs 4 and 6 was greater than 3.0 indicating that

when used with other independent variables in an

equation, the coefficient for air content of concretes made of NAE cements may be highly sig- nificant. In eqs 4A, 4B, 6A, and 6B, there were

instances where NaoO and Pb had coef./s.d. ratios

less than 1.0 in one or the other of the equations

for the smaller groups of cement.

The estimated contributions and range of contributions to the percentage weight loss (AWTL)

in the freezing-and-thawing tests at the time of 40 percent reduction of dynamic modulus of the

concretes of 5 + 1-in slump, as calculated from

the coefficients of eq 4, table 11-15, are presented

in table 11-16. Tables 11-15 and 11-16 show that

increases in air content, C3A, and C4AF were asso- ciated with increase in AWTL. Increases in K2O,

and probably Mn, Rb, and Ti were associated

with decrease in AWTL. The coefficients for Na20

and Pb were of doubtful significance.

6.3. Saturation Ratio

6.3.1. Saturation Ratio of Series O Concretes

As previously indicated in subsection 3.3, the

concrete specimens, moist-cured for 14 days, then

dried in laboratory air for 4 weeks, were placed in water at 40 °F for 24 hours prior to the start of the freezing-and-thawing tests. Determinations were made of the air content of the freshly-mixed

concrete, the loss of weight as a result of drying,

and the weight gain after the 24 hours in water. The ratio of this weight gain to the possible weight

gain if completely saturated, i.e., the volume of water lost in drying plus the volume of air, was

calculated and is here termed the saturation ratio. The frequency distribution of the saturation

ratios is presented in table 11-17 for Series 0

concretes. The values for the ratio (OSAT) ranged

from less than 0.3 to more than 0.8. All of the

concretes made with the AE cements (Types lA,

IIA, and IIIA) had very low ratios, and the

values for the concretes made with the different

types of NAE cements overlapped.

Selected equations presented in table 11-18

indicate the relationship of various independent

variables to the saturation ratio (OSAT) for the

AE + NAE cements. As indicated in eqs 1 and 2, the ratio is significantly related to the air content

(OAIR) of the concretes. A smaller S.D. value was obtained in eq 2 which used the square root

of the air content as an independent variable in

place of the air content as in eq 1. The additional use of C2S and C4AF in eq 3 resulted in a significant reduction in variance. (See table 11-27.) The

reduction in variance resulting from also using

MgO and Loss in eq 4 was significant at the 1.0 percent level. Comparing eqs 2 and 4 indicated an

overall reduction in variance significant at the

1.0 percent level. With the added trace elements

Cu, Mn, P, and Rb in addition to commonly determined variables in eq 5 there was a reduction

in variance significant at the 1.0 percent level. (See table 11-27.)

Table 11-17. Frequency distribution of cements with respect to the ratio of the volume water absorbed when placed in water for

2i. hours divided by the volume water lost after 28 days drying in laboratory air, plus the volume of air in the concrete. The

concretes were made with a water-cement ratio of 0.635 (OSAT)

Type cement

Saturation ratio

0.25

to 0.30

0.30

to 0.35

0.35

to 0.40

0.40

to

0.45

0.45

to 0.50

0.50

to 0.55

0.55

to 0.60

0.60

to 0.65

0.65

to

0.70

0.70

to 0.75

0.75

to 0.80

0.80 and

over Total

Number of cements

I 13

3

3

11 11 29 17 11 1 1 82

868

320

315

lA 4 1 11 3 8 18 21 11 2 2 IIA

III 2 7 4 6 1 IIIA 1 1 1 IV, v 2 3 4 3 3

Total . 5 2 10 13 21 43 44 36 16 5 3 199

17
Table 11-18. Coefficients for equations for AE + NAE cements relating the saturation kubic yard and a water-cement ratio of 0.635

Eq. No.

1

2

3 -.-

4

5

5A

5B

6

7

7A

73

Note Const.

OSAT

s.d. = +0.6745 = (0.0073) OSAT

s.d. = +0.7987 = (0.0133) OSAT

s.d. = +0.6288 = (0.0243) OSAT

s.d. = +0.5879 = (0.0285) OSAT

s.d. = +0.5858 = (0.0283) OSAT (odd)

s.d. = +0.6197 = (0.0447) OSAT (even)

s.d. = +0.5628 = (0.0381) OSAT

s.d. = +1.486

(0.223) OSAT

s.d. = +1.734 = (0.234) OSAT (odd)

s.d. = +1.363 = (0.365) OSAT (even)

s.d. = +2.126 = (0.318)

OAIR

-0.0396

(0.0026)

(OAIR)° =

-0.1522

(0.0092) -0.1406

(0.0079) -0.1430

(0.0079) -0.1447

(0.0077) -0.1376

(0.0115) -0.1524

(0.0104) -0.1434

(0.0079) -0.1465

(0.0078) -0.1394

(0.0114) -0.1553

(0.0109)

C2S

+0.00409 +0.00538

(0.00054) (0.00173) +0.00440 +0.00574

(0.00055) (0.00171) +0.00441 +0.00537

(0.00055) (0.00176) +0.00416 +0.00480

(0.00078) (0.00283) +0.00455 +0.00624

(0.00082) (0.00232)

C4AF

Note 1, 178 cements, Avg. = 0.5911, S.D. = 0.0963 Note 2, 89 cements

*Coef./s.d. ratio less than 1.0.

Table 11-19. Coefficients for equations for NAE cements relating the saturation ratio and a water-cement ratio of 0.635 to

Eq. No.

1.-

2..

3..

4..

5..

6A

5B

6..

7..

7A

7B

Note Const.

OSAT

s.d. = +0.7122 = (0.0115) OSAT

s.d. = +0.8175 = (0.0209) OSAT

s.d. = +0.6400 = (0.0296) OSAT

s.d. = +0.5983 = (0.0342) OSAT

s.d. = +0.6023 = (0.0338) OSAT

s.d. (odd) = +0.6247 = (0.0567) OSAT

s.d. (even) = +0.5777 = (0.0428) OSAT

s.d. = +1.411 = (0.231) OSAT

s.d. = +1.674

== (0.241) OSAT

B.d. (odd) = +1.482 = (0.336) OSAT

s.d. (even) = +1.937 = (0.347)

OAIR

-0.0633

(0.0063)

(OAIR)o-6

-0.1676

(0.0162) -0.1475

(0.0140) -0.1464

(0.0139) -0.1526

(0.0144) -0.1485

(0.0255) -0.1567

(0.0174) -0.1475

(0.0138) -0.1552

(0.0144) -0.1550

(0.0243) -0.1605

(0.0178)

CjS

+0.00396 +0.00541

(0.00056) (0.00180) +0.00426 +0.00572

(0.00058) (0.00178) +0.00426 +0.00523

(0.00058) (0.00184) +0.00462 +0.00415

(0.00081) (0.00302) +0.00354 +0.00723

(0.00085) (0.00235)

C4AF

Note 1, 166 cements, Avg. = 0.6070, S.D. = 0.07757 Note 2, 88 cements

*Coef./s.d. ratio less than 1.0.

18
ratio at the start of the freeze-thaw tests of concretes of nominal 6 ]4 bags cement per

to various independent variables (OSAT)

SiOi FetOa MgO Loss Cu Mn Ni P Rb S.D.

0.06376

0.06023

0.05011

+0.00612

(0.00319) +0.00936

(0.00324)

* +0.00489

(0.00512) +0.01238

(0.00435)

+0.01483

(0.00715) +0.01660

(0.00707)

* +0.00334

(0.01113) +0.02943

(0.00948)

0.04932

+0.9163

(0.4522) +0.7838

(0.6849) +1.3715

(0.6409)

-0.0631

(0.0452)

* -0.0419

(0.0440) -0.0885

(0.0459)

+0.0442

(0.0341)

* +0.0205

(0.0526) +0.0599

(0.0465)

-3.653

(1.952) -5.557

(2.657) *-1.195

(3.061)

0.04792

0.05070

0.04561

+0.02271

(0.00309) +0.02134

(0.00316) +0.02472

(0.00470)

* +0.01798

(0.00468)

+0.01239

(0.00547) +0.00946

(0.00575) +0.01008

(0.00898)

* +0.00507

(0.00777)

0.04912

+0.9583 • (0.4524) +1.0170

(0.6775) +1.2872

(0.6753)

-0.0529

(0.0315)

* -0.0268

(0.0436) -0.0799

(0.0479)

-1.354

(1.151)

* -0.616

(1.624) -1.997

(1.818)

+0.0453

(0.0343)

* +0.0290

(0.0526)

* +0.0361

(0.0477)

-3.163

(2.014) -4.345

(2.776)

* -1.251

(3.175)

0.04787

0.04997

0.04659

at the start of freeze-thaw tests of concretes of nominal 5 K bags cement per cubic yard

various independent variables (OSAT)

SiO: Fe203 MgO Loss Cu Mn Ni P Rb S.D.

0.06124

0.06055

0.05077

+0.00550

(0.00330) +0.00885

(0.00332) +0.00550

(0.00496) +0.02111

(0.00456)

+0.01397

(0.00752) +0.01601

(0.00737)

* +0.01043

(0.01231) +0.02489

(0.00938)

0.05016

+0.982

(0.473)

* +0.670

(0.757) +1.297

(0.601)

-0.0726

(0.0327) -0.0624

(0.0438) -0.1012

(0.0512)

+0.0488

(0.0348)

* +0.0123

(0.0555) +0.0768

(0.0456)

-3.35

(2.05) -4.79

(2.96) *-1.70

(3.07)

0.04847

0.05123

0.04556

+0.02242

(0.00322) +0.02092

(0.00328) +0.02807

(0.00467) +0.01255

(0.00462)

+0.01307

(0.00567) +0.00962

(0.00599)

* +0.00592

(0.00922) +0.01228

(0.00782)

0.04973

+1.019

(0.471)

* +0.643

(0.724) +1.522

(0.613)

-0.0599

(0.0329) -0.0458

(0.0423) -0.0796

(0.0532)

* -1.162

(1.175)

* +0.036

(1.792) -2.170

(1.578)

+0.0502

(0.0350)

* +0.0244

(0.0535) +0.0598

(0.0470)

-2.78

(2.11) -2.85

(3.03) *-2.72

(3.12)

0.04833

0.04926

0.04633

19
Table 11-20. Calculated contributions of independent vari- ables to the saturation ratio at the start of the freeze-thaw

tests of concretes of nominal 5 34 bags cement per cubic yard

and a water-cement ratio of 0.635 (.OSAT)

Independent

variables Range of variables

(percent)

Coefficients from eq 5 table 11-19

Calculated

contributions

to OSAT

Calculated range of contribution to OSAT

Const. = +0.60

(OAIR)»-5 NAE cements. 0 to 2.12 -0.1526 0 to -0.32 0.32 C2S 5 to 50 +0.00426 +0.02 to +0.21 0.19 CiAF 1 to 16 +0.00523 +0.01 to +0.08 0.07 MgO 0 to 5.0 +0.00885 0 to +0.04 0.04 Loss . _ 0.3 to 3.3 +0.01601 0 to +0.05 0.05 Cu 0 to 0.05 +0.982 0 to +0.05 0.05 Mn 0 to 1 -0.0726 0 to -0.07 0.07 p** 0 to 0.5 +0.0488 0 to +0.02 0.02 Rb** 0 to 0.01 -3.35 0 to -0.03 0.03

** Coefficient of doubtful significance as coef./s.d. ratio less than 2.0. Equation 6 was calculated using the oxides,

CaO, Si02, and Fe203 as independent variables

instead of the potential compounds. MgO and

Loss had coef./s.d. ratios of less than 1.0 and were

not included. The reduction in variance was highly

significant. With the added trace elements Cu,

Mn, Ni, P, and Rb (eq 7), the reduction in vari- ance was significant at the 5.0 percent level. (See

table 11-27.)

In equations calculated for the "odds" and

"evens" in the array of cements, (eqs 5A, 5B, 7A,

and 7B), the coef./s.d. ratios for Fe203, MgO, Loss,

Mn, Ni, P, and Rb were less than 1.0 in one or the other of the pairs of equations for the smaller

groups of cement.

The equations presented in table 11-19 for the

relation of the various independent variables to the saturation ratio of NAE cements are very

similar to, and the coefficients and coef./s.d. ratios

reasonably consistent with those presented in table 11-18 where the AE cements were included.

The coefficients for the air content or square root

of the air content (eqs 1 and 2) were highly significant even with the NAE cements. (See table

11-27.) The additional use of C.S and C4AF in eq 3 resulted in a highly significant reduction in variance, but with the addition of MgO and Loss

in eq 4 the reduction in variance was not significant at the 5.0 percent level. The use of trace

elements Cu, Mn, P, and Rb (eq 5) caused a

reduction in variance significant at the 1.0 per- cent level, but when these plus Ni were used with

the oxides (eq 7), the added reduction in variance was significant only at the 5.0 percent level. In

the equations for the "odds" and "evens" (eqs 5A,

5B, 7A, and 7B) there were instances where FeaOs,

Loss, Cu, Ni, P, and Rb had coef./s.d. ratios less than 1.0 in one or more of the equations for the

smaller groups.

.

The estimated contributions and range of contributions to saturation ratio of the constant w/c

concretes, as calculated from the coefficients of eq 5, table 11-19, are presented in table 11-20. Increase in air content and probably Mn were

associated with a decrease in the saturation ratio, Increases in C2S and probably C4AF, MgO, Loss,

and Cu were associated with increases of the

saturation ratio.

6.3.2. Saturation Ratio of Series A Concretes

The frequency distribution of the saturation

ratios of the Series A concretes is presented in table 11-21. The AE cements (Types lA, IIA,

and IIIA) had low saturation ratios (0.20 to 0.45)

whereas the NAE cements had ratios of 0.4 to more than 0.8. There was a broad overlapping of the ratios for the different types of NAE cements.

Equations indicating the various independent

variables associated with the saturation ratio of

AE + NAE cements are presented in table 11-22.

The use of the square root of the air content

(eq 2) resulted in a slightly lower S.D. value than

when using the air content (eq 1). When the w/c

required to produce the 5 + 1-in slump concrete was included as a single additional variable in eq 3, the coefficient for w/c was not significant.

In eq 4 where C2S and C4AF were added as independent variables, the coefficient for w/c was

positive and significant at the 5.0 percent level. The use of the commonly determined variables

C2S, C4AF, C3A/SO3, MgO, and Loss (eq 5) re- sulted in a highly significant reduction in variance.

(See table 11-27.) The use of Co, Ni, P, Rb, and

Zr together with commonly determined variables

Table 11-21. Frequency distribution of cements with respect to the ratio of the volume water absorbed when placed in water for 2U

hours divided by the volume water lost by drying for 28 days in laboratory air plus the volume of air in the concrete. The concretes were made with a slump of 5 ± 1 inches (ASAT)

Saturation ratio

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 Type cement to to to to to to to to to to to to and Total

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 Over

Number of cements

I 2

2

2

1

8 17 17 15 10 7 2 1 79

867

320

315

ia 1 4 1 II 3 5 5 16 15 15 4 2 IIA 1 1 III 2 4 7 5 1 1 IIIA 1 1 1 IV, V 2 5 4 2 2 Total 1 1 6 3 7 13 26 31 41 30 24 9 3 195

20
(eq 6) resulted in a highly significant reduction in variance. (See table 11-27.) The use of the oxides

(eq 7), or the oxides with trace elements (eq 8)

resulted in S.D. values and reduction of variance

comparable with those obtained using the potential compounds in eqs 5 and 6. In equations for the "odds" and "evens" (eqs

6A, 6B, 7A, and 7B) there were instances where

C3A/SO3, Fe203, K2O, MgO, Co, Rb, and Zr had

coef./s.d. ratios less than 1.0 in one or the other

of the pairs of equations with the smaller groups

of cements.

The corresponding series of equations for NAE

cements is presented in table 11-23. The results are in reasonable agreement with those presented

in the previous table 11-22, where the AE cements

were included.

In eq 4A and 4B the coef./s.d. ratios of AI2O3,

Fe203, Cr, and V had coef./s.d. ratios less than

1.0 in one or the other of the equations for the

smaller groups of cements, the "odds" and "evens."

The estimated contributions and range of contributions to saturation ratio of the constant

slump concretes, as calculated from the coeffi- cients of eq 6, table 11-23, are presented in table

11-24. Increases in air content, and probably

C3A/SO3, Ni, and Rb were associated with decreases in the saturation ratio. Increases in C2S,

MgO, and probably C4AF, Loss, and P were asso- ciated with increases of the saturation ratio.

6.4. Cycles of Freezing and Thawing

Frequency distributions of the number of cycles

required to cause a 40-percent reduction of dynamic modulus of Series 0 and Series A concretes

are given in tables 11-25 and 11-26, respectively.

No analyses of these data were made because of

the fact that the distribution curves for these data

and those for durability factor are identical except

for the air-entraining cements, and, therefore,

equations, especially with NAE cements, would

have shown the same relationships. For specimens

which fail in 300 cycles or less, the durability fac- tor is exactly one-fifth the number of cycles at which the 40-percent reduction in dynamic E is reached. All of the non-air-entrained specimens

failed in 300 cycles or less, and thus the distribution curves are the same for dynamic E and

number of cycles up to this point. (There are some

discrepancies in the distributions given in tables

11-25 and 11-26 as compared to tables 11-1 and

11-5 due to the fact that the durability factors were rounded to the nearest unit and the numbers

of cycles were taken to the nearest cycle. The three

non-air-entrained cements shown in the 300-500

cell in table 11-26 were ones which failed at 300

cycles). Although the two distributions are differ- ent for specimens which do not fail in 300 cycles,

the small number of air-entraining cements did

not warrant further analysis using the number of cycles instead of the durability factor.

6.5. Autogenous Healing

After completion of the freezing-and-thawing

tests, the deteriorated specimens were placed in the fog room. At various periods ranging from

approximately one to approximately five years, the specimens were removed from the fog room

and retested for dynamic modulus.

The periods during which the specimens were

stored in the fog room after freezing-and-thawing

tests were nominally 1, 2, 3, 4, and 5 years. However, due to the fact that large groups of specimens

which had been removed from freezing and thawing at different times were retested for dynamic

modulus at the same time, the actual amount of time in storage varied within each nominal age

group.

The ranges of actual elapsed times in months

are given in table 11-28. All of the specimens in the 4-year category were specimens which had

been retested at 2 or 3 years, then were placed in the fog room and retested a second time at 4 years. A small number of these were retested a third

time and are included with the 5-year group.

Since it appears, as is shown below, that practically all of the autogenous healing that occurred

took place in the first year, and no statistical intercomparisons of data are made between years,

it seems the variations in time within the nominal

age groups do not affect the results. Table 11-29 shows the averages and standard

deviations of the ratios of dynamic modulus after autogenous healing to dynamic modulus at the

end of the freezing-and-thawing test. Most of the

specimens achieved calculated dynamic modulus

values equal to or higher than the original dynamic modulus, but the moduli for these two

periods could not be compared directly, because

of the sloughing and consequent changes in di- mensions that many of the specimens underwent

during freezing-and-thawing. For the period of autogenous healing, however, the dimensions did

not change. Also changes in weight during the

healing period were negligible.

For the NAE cements alone, the average ratio

for all five age groups was 2.32, while the average

for the 42 specimens measured at one year was

2.38. Thus all the autogenous healing evidently

occurred before 16 months. It seems probable that

the length of time required for recovery was actually less than one year, but how much less is not

known.

The ratios for the air-entrained specimens were

significantly lower than those for the non-airentrained specimens, an average of 1.34 for both

2- and 3-year storage compared to 2.32 for the

non-air-entrained concretes. The air-entrained

specimens had lower dynamic modulus values at the start of the freezing-and-thawing tests. However, the air-entrained specimens generally appeared to regain a smaller percentage of their

original dynamic modulus during storage. The

ratios of calculated dynamic modulus after storage

21
Table 11-22. Coefficients for equations for AE + NAE cements relating the saturation

cubic yard and a slump of 5 + 1 inch to

Eq. No.

1

2

3

4

6

6

6A

6B

7

8

8A

8B

Note Const.

ASAT

s.d. = +0.6827 = (0.0067) ASAT

s.d. = +0.8119 = (0.0105) ASAT

s.d. = +1.0550 = (0.1814) ASAT

s.d. = +0.2505 = (0.1726) ASAT

s.d. = +0.2258 = (0.1647) ASAT

s.d. = +0.2441 = (0.1583) ASAT (odd)

s.d. = +0.3459 = (0.2752) ASAT (even)

s.d. = +0.1735 = (0.1913) ASAT

s.d. = +1.419 = (0.302) ASAT

s.d. = +1.474 = (0.293) ASAT (odd)

s.d. = +1.285 = (0.504) ASAT (even)

s.d. = +1.844 = (0.389)

AAIR

-0.0429

(0.0023)

(AAIR)o-s

-0.1657

(0.0074) -0.1774

(0.0114) -0.1415

(0.0103) -0.1441

(0.0100) -0.1456

(0.0096) -0.1510

(0.0173) -0.1429

(0.0116) -0.1387

(0.0103) -0.1413

(0.0100) -0.1502

(0.0184) -0.1416

(0.0126)

w/c

-0.3576

(0.2664) +0.5867

(0.2391) +0.6212

(0.2317) +0.5880

(0.2229) +0.4931

(0.3880) +0.6140

(0.2676) +0.6888

(0.2377) +0.6508

(0.2303) +0.4515

(0.4103) +0.6703

(0.2845)

CsS C4AF

+0 00443 +0 00464

(0 00049) (0 00164) +0 00448 +0 00358

(0 00050) (0 00174) +0 00468 +0 00408

(0 00048) (0 00169) +0 00435 +0 00440

(0 00066) (0 00251) +0 00495 +0 00419

(0 00074) (0 00249)

Note 1, 177 cements, Avg. = 0.5961, S.D. = 0.1097 Note 2, 89 cements Note 3, 88 cements

*Coef./s.d. ratio less than 1.0.

Table 11-23. Coefficients for equations for NAE cements relating the saturation ratio and a slump of 5 ± 1 inch to vari

Eq. No

1

2

3

4

5

6

6A

6B

7

8

8A

8B

Note Const. AAIR (AAIR)<i-5 w/c CaS C4AF

ASAT

s.d. = +0.7286 = (0.0086) ASAT

s.d. = +0.8288 = (0.0147) ASAT

s.d. = +1.1607 = (0.1819) ASAT

s.d. = +0.3426 = (0.1751) ASAT

s.d. = +0.3201 = (0.1664) ASAT

s.d. = +0.3504 = (0.1609) ASAT (odd)

s.d. = +0.4760 = (0.2919) ASAT (even)

s.d. = +0.2080 = (0.2032) ASAT

s.d. = +1.380 = (0.307) ASAT

s.d. = +1.469 = (0.298) ASAT (odd)

s.d. = +1.980 = (0.486) ASAT (even)

s.d. = +1.287 = (0.405)

-0.0740

(0.0049) -0.1804

(0.0119) -0.1945

(0.0141) -0.1626

(0.0122) -0.1628

(0.0116) -0.1607

(0.0115) -0.1712

(0.0191) -0.1489

(0.0152) -0.1567

(0.0118) -0.1571

(0.0116) -0.1651

(0.0184) -0.1488

(0.0153)

-0.4915

(0.2685) +0.4887

(0.2439) +0.5422

(0.2349) +0.4814

(0.2271)

* +0.3351

(0.4160) +0.6246

(0.2820) +0.6202

(0.2436) +0.5556

(0.2367)

* +0.1914

(0.4083) +0.7876

(0.2991)

+0 00428 +0 00449

(0 00050) (0 00162) +0 00419 +0 00302

(0 00051) (0 00172) +0 00436 +0 00353

(0 00049) (0 00168) +0 00421 +0 00351

(0 00070) (0 00273) +0 00460 +0 00426

(0 00007) (0 00237)

Note 1, 165 cements, Avg. = 0.6152, S.D. = 0.0851 Note 2, 83 cements Note 3, 82 cements

*Coef./s.d. ratio less than 1.0.

22
ratio at the start of the freeze-thaw tests of concretes of nominal 5 H ix'^QS cement per

various independent variables (ASAT)

CaO Si02 FeiOs K2O MgO Loss Co Ni P Rb Zr S,D.

0.06400

0.06596

0.06583

0.04483

+0.00926

(0.00291) +0.00868

(0.00276)

* -0.00025

(0.00428) +0.01675

(0.00366)

+0.01335

(0.00689) +0.01651

(0.00625) +0.01539

(0.00885) +0.02155

(0.00962)

0.04273

+4.76

(2.27) *+0.44

(5.55) +5.96

(2.52)

-2.653

(0.991) -3.627

(1.507) -1.678

(1.384)

+0.0540

(0.0293) +0.0640

(0.0516) +0.0476

(0.0360)

-4.64

(1.69) -3.19

(2.48) -6.38

(2.48)

-0.0880

(0.0780) -0.1360

(0.0858)

* +0.4208

(0.6572)

0.04062

0.04238

0.03846

-0.0251

(0.0032) -0.0256

(0.0031) -0.0205

(0.0047) -0.0313

(0.0044)

+0.0235

(0.0030) +0.0241

(0.0030) +0.0238

(0.0041) +0.0236

(0.0045)

+0.00825

(0.00505) +0.00930

(0.00500) +0.01403

(0.00801)

* +0.00272

(0.00713)

-0.0424

(0.0176) -0.0398

(0.0186) -0.0558

(0.0281)

* -0.0201

(0.0269)

0.04171

+4.18

(2.22) -0.86

(5.39) +5.48

(2.47)

-2.847

(0.968) -3.867

(1.477) -1.877

(1.355)

+0.0520

(0.0286) +0.0737

(0.0502) +0.0452

(0.0353)

-3.15

(1.82) *-1.39

(2.59) -5.99

(2.77)

-0.1167

(0.0759) -0.1576

(0.0830)

* +0.3715

(0.6440)

0.03988

0.04144

0.03848

at the start of freeze-thaw tests of concretes of nominal 5 bags cement per cubic yard

ous independent variables (ASAT)

CaO Si02 FeiOi K2O MgO Loss Co Ni P Rb Zr S.D.

0.05509

0.05488

0.05449

0.04395

+0.00881

(0.00279) +0.00827

(0.00276) +0.00668

(0.00412) +0.01036

(0.00418)

-0.01064

(0.00648) +0.01452

(0.00636) +0.01351

(0.00951) +0.01518

(0.00953)

0.04175

+4.46

(2.30) *+3.22

(4.24) +4.76

(2.91)

-2.244

(0.993)

* -1.573

(1.827) -2.390

(1.212)

+0.0625

(0.0290) +0.0968

(0.0535) +0.0400

(0.0365)

-4.10

(1.70) -5.08

(2.67) -2.69

(2.33)

-0.0980

(0.0772) -0.0906

(0.0901) -0.2232

(0.2066)

0.03993

0.04268

0.03901

-0.0235

(0.0032) -0.0242

(0.0031) -0.0267

(0.0044) -0.0248

(0.0048)

+0.0235

(0.0031) +0.0237

(0.0031) +0.0203

+0.00837

(0.00504) +0.00918

(0.00500)

* +0.00658

(0 008171

-0.0344

(0.0180) -0.0353

(0.0190) -0.0942

(0.0304)

* +0.0077

(0.0251)

0.04085

+3.97

(2.26) *+3.71

(4.02) +3.97

(2.80)

-2.390

(0.968) -2.413

(1.717) -2.169

(1.179)

+0.0596

(0.0283) +0.1085

(0.0501) +0.0465

(0.0354)

-2.80

(1.83) *-2.36

(2.65) -3.17

(2.57)

-0.1310

(0.0749) -0.1495

(0.0835) -0.2426

(0.2003)

0.03919

0.04003

+0.0259 +0.00765

(0.0047) (0.00669) 0.03818

23
to that at the beginning of freezing and thawing

ranged from approximately 0.95 to less than 0.70,

while those for the non-air-entrained specimens

ranged from approximately 0.9 to 1.9. For the

Table 11-24. Calculated contributions of independent vari- ables to the saturation ratio at the start of the freeze-thaw

tests of concretes of nominal 5 Vi bags cement per cubic yard

and a slump of 5 ± 1 inch. (ASAT)

Independent

variables Range of variable

(percent)

Coefficients from eq 6 taDie 11—

Calculated

contributions

i-^ lO AoA A Q A T1

Calculated range of contributions to ASAT

Const. = +0.35

(AAIR)»-5 NAE cements. 0 to 2.23 -0.1607 0 to -0.36 0.36 w/c_- 0.6 to 0.7 +0.4814 +0.29 to +0.34 0.05 C2S... __ 5 to 50 +0.00436 +0.02 to +0.22 0.20 C4AF 1 to 16 +0.00353 0 to +0.06 0.06 C3A/SO3 0.4 to 10.1 -0.00585 -0.02 to -0.06 0.04 MgO 0 to 5.0 +0.00827 0 to +0.04 0.04 Loss . _

.

0.3 to 8.3 +0.01452 0 to +0.05 0.05 Co** 0 to 0.01 +4.46 0 to +0.04 0.04 Ni 0 to 0.02 -2.244 0 to -0.04 0.04 P 0 to 0.5 +0.0625 0 to +0.03 0.03 Rb 0 to 0.01 -4.10 0 to -0.04 0.04 Zn** 0 to 0.5 -0.098 0 to -0.05 0.05

** Coefficient of doubtful significance as coef./s.d. rati o was less than 2.0.

non-air-entrained concretes alone the ones that

regained the greatest amounts in dynamic modulus were generally those that had lower original

dynamic modulus values.

The evaluation of autogenous healing was fur- ther complicated by the fact that the specimens were seldom removed from freezing and thawing

at exactly 60 percent of original E. A few were removed at 60 to 65 percent Eq while others which

were deteriorating rapidly were below 20 percent

£"0 when removed. The latter were specimens

which failed during the first freezing-and-thawing

period and were first checked at 10 cycles. They

were also specimens which showed a weight gain

during freezing and thawing due to early failure. However, even these specimens reached higher

dynamic modulus values after storage than they

had before freezing and thawing.

No multivariable equations are given relating

independent variables to regain of dynamic modulus. However, the data were subjected to analysis

of variance to determine if there were significant

differences in the ratios between cements. The

results are shown in table 11-30 for the different

Table 11-25. Frequency distribution of cements with respect to OCYS, the number of cycles of freezing and thawing required to cause a iO-percent reduction in dynamic modulus of Series 0 concretes

Number of cycles

0 20 40 60 80 100 150 200 300 500 700 Type cement to to to to to to to to to to to Total 20 40 60 80 100 150 200 300 500 700 1000

Number of cements

I 1 7 7 7 14 28 13 5 82

868

320

315

lA 5 3

II 1 8 5 9 12 24 5 4 IIA 1 2

III 3 2 2 2 4 3 4 IIIA 1 2 IV, v 1 2 4 1 4 3

Total 3 20 18 19 32 59 21 13 6 6 2 199

Table 11-26. Frequency distribution of cements with respect to ACYS, the number of cycles of freezing and thawing required to cause a l^O-percent reduction in dynamic modulus of Series A concretes

Number of cycles

0 20 40 60 80 100 150 200 300 500 700 Type cement to to to to to to to to to to to Total 20 40 60 80 100 150 200 300 500 700 1000

Number of cements

I 2 5 2 13 15 21 14 6

12

13

12

1

79

8 67

320

3

15

lA 4

11 1 8 4 7 13 25 6 IIA 1 in 1 1 2 1 2 6 2 4 IIIA 1 2 IV, V 1 1 3 3 4 1 2 Total 5 15 11 24 34 53 24 13 8 6 2 195

24
Table 11-27. "F" values for significance of reduction of

variance due to added variables.

Critical "F" ratios Table Equations* ..p., D.F.

ratio a = 0.01 a = 0.05

11-2 0,1 118 2:177 4.70 3.04

0,2 76.4 2:177 4.70 3.04

1,3 15.1 6:171 2.91 2.15

3,4 5.48 5:166 3.13 2.27

1,5 17.8 5:172 3.12 2.27

5,6 5.76 5:167 3.13 2.27

11-3 0,1 6.83 2:166 4.72 3.04

0,2 19.0 2:166 4.72 3.04

1,3 9.04 6:160 2.92 2.15

3,4 4.01 5:155 3.14 2.27

1.5 10.5 5:161 3.12 2.27

5,6 4.25 5:156 3.14 2.27

11-6 0,1 118 2:173 4.71 3.04

0,2 87.6 2:173 4.71 3.04

1,3 21.8 4:169 3.42 2.43

3,4 4.37 5:164 3.13 2.27

1,5 12.5 4:169 3.42 2.43

5,6 3.63 6:163 2.92 2.15

11-7 0,1 8.05 2:162 4.72 3.04

0,2 20.4 2:162 4.72 3.04

1,3 10.7 4:158 3.43 2.43

3,4 3.53 5:153 3.14 2.27

1,5 11.2 4:158 3.43 2.43

5,6 3.07 6:152 2.92 2.15 U-10 0,1 21.0 2:178 4.70 3.04

1,2 18.9 4:174 3.14 2.43

2,3 5.9 4:170 3.14 2.43

1,4 13.1 6:172 2.91 2.15

4,5 4.95 5:167 3.13 2.27

11-11 0,1 0.92 2:166 4.72 3.04

1,2 17.2 4:162 3.14 2.43

2,3 6.46 4:158 3.14 2.43

1,4 12.0 6:160 2.92 2.15

4,5 5.46 5:155 3.14 2.27

11-14 0,1 3.46 2:174 4.71 3.04

0,2 9.09 2:174 4.71 3.04

2,3 16.5 4:170 3.14 2.43

3,4 4.46 4:166 3.14 2.43

16.6 4:170 3.14 2.43

5,6 4.48 4:166 3.14 2.43

11-15 0,3 10.3 6:158 2.92 2.15

3,4 5.20 4:154 3.14 2.43

0,5 10.3 6:158 2.92 2.15

5,6 5.21 4:154 3.14 2.43 11-18 0,1 115 2:176 4.71 3.04 140 2 :176 4.71 3.04

2,3 40.1 2:174 4.71 3.04

3,4 3.81 2:172 4.71 3.04

2,4 22.6 4:172 3.14 2.43

4.5 3.55 4:168 3.14 2.43

2,6 30.5 3:173 3.88 2.67

6,7 2.83 5:168 3.13 2.27 11-19 0,1 51.1 2:164 4.71 3.04

n 9 54.2 2 :164 4.71 3.04

2,3 35.6 2:162 4.71 3.04

3,4 2.98 2:160 4.71 3.04

2,4 19.7 4:160 3.42 2.43

4,5 3.84 4:156 3.42 2.43

2,6 27.4 3:161 3.88 2.67

6,7 2.58 5:156 3.13 2.43 11—22 n 1 173 2:175 4.70 3.04

0,2 253 2:175 4.70 3.04

2,4 33.6 3:172 3.88 2.67

4,5 6.77 3:169 3.88 2.67

5,6 4.60 5:164 3.13 2.27

3,7 35.4 4:170 3.42 2.43

7,8 4.18 5:159 3.17 2.27 11-23 0,1 115 2:163 4.72 3.04

0,2 117 2:163 4.72 3.04

2,4 31.4 3:160 3.88 2.67

4,5 6.77 3:157 3.88 2.67

5,6 3.93 5:152 3.14 2.43

3,7 32.6 4:158 3.43 2.43

7,8 3.73 5:153 3.14 2.43

* 0 in the equation column refers to the D.D. value of the corresponding dependent variable as given in footnotes in the tables of equations.

Table 11-28. Autogenous healing—actual elapsed time

XT I Nominal time» years Actual elapsed time, months

1 16.1 to 16.4

20.1 to 24.8

33.2 to 38.2 48.9 to 51.2 57.5 to 60.4

2

3

45...

Table 11-29. Autogenous healing—average ratios of dynamic

modulus after storage to that after freezing and thawing

Time, Cement n Average S.D.

years type

1 NAE 42 2.38 0.60 2 NAE 477 2.34 1.46

3 NAE 302 2.20 0.82 4 NAE 59 2.81 1.81

5 NAE 24 2.15 1.78 2 AE 31 1.34 0.14 3 AE 14 1.32 0.14

Table 11-30. Autogenous healing—ANOVA for differences between cements—ratio of dynamic nrndulus

Time,

years Cementtype n S.S. M.S. F Fcrit.

1 NAE

NAE

NAE

NAE

AE

AE

Between cements. Within cements.

Total

827

35

109 330

439

69 210

279

415

19

51823

310

13

8.7578

4.2729 13.0307

480.643

140.984

621.627

108.240

90.559 198.799

29.0017

45.9077 74.9094

0.0869

0.2637 0.3506

0.2485

0.0540 0.3025

1.0947 0.15836.92 2.30

2 Between cements. Within cements. _ Total4.4096

0.4272

10.32 1.30

3 Between cements. Within cements _

.

Total Between cements. Within cements.

Total

1.5687 0.43123.64 1.37

5 7.2504 3.0605

2.37 3.06

2 Between cements. Within cements..

Total

0.0174

0.0146

1.19 2.77

3 Between cements. Within cements..

Total

0.0828

0.0054

15.33 3.71

1

nominal ages for air-entrained and non-airentrained cements.

There were no significant differences between

the 0-series and A-series concretes within ce- ments. Therefore the data for the four specimens

for each cement were combined in determining

the within-cement variance. The critical values in column 8 headed F crit. are those which must be

equalled or exceeded by the F ratios in column 7

to indicate a significant difference between ce- ments at the 5.0 percent significance level. For the non-air-entrained cements, there were

significant differences at the nominal 1-, 2-, and

3-year periods of storage, but not at 5 years. The

data for 4 years could not be subjected to this

analysis because they did not include groups from

the same cement, but were mainly individual

values.

For the air-entrained cements a significant dif- ference was indicated at 3 years but not at 2.

25
7. Discussion

7.1. Durability

Tables 11-31 amd 11-32 show selected equations for the various independent variables for the

Table 11-31. Coefficients, coef./s.d. ratios and calculated contributions of independent variables associated with

durability, weight loss, and saturation ratio (Series O

concretes made of AE + NAE cements)

Column

Eq. No.

Table No. Dependent variable Constant

Air content, coef.. coef./s.d Calculated range.

CiA, coef

coef./s.d Calculated range.

CsS, coef

coef./s.d Calculated range.

C2S, coef

coef./s.d Calculated range. CiAF, coef

coef./s.d Calculated range. NaiO, coef

coef./s.d Calculated range. K2O, coef

coef./s.d Calculated range. MgO, coef

coef./s.d... Calculated range. APF, coef

coef./s.d Calculated range.

Loss, coef

coef./s.d Calculated range.

Ba, coef

coef./s.d Calculated range. Cu, coef

coef./s.d Calculated range. Mn, coef

coef./s.d Calculated range.

P, coef

coef./s.d Calculated range. Pb, coef

coef./s.d Calculated range. Rb, coef

coef./s.d Calculated range.

Ti, coef

coef./s.d Calculated range.

Zr, coef... coef./s.d Calculated range.

>(OAIR)»

11-3 ODUR

+88.6

+8.89

20.8 89

-0.53

1.9 24 -0.817

3.1 37

-8.26

1.9 6 -20.3

4.8 22 -2.75

3.9 14 -0.0031

2.1

9

-40.2

1.9

-210

2.5 11

-208

1.8 10 -1068

2.5 11 -14.0

2.3

1.4

11-12 OWTL

-1.15

+1.42

10.0

14.2 +0.411

4.0

5.8

+0.753

5.7 11 -3.71

2.5

2.6 -8.44

6.3

9.3

-86

2.1

4.3 -315

2.6

3.2 -6.35

3.1

6.4 +11.2

1.8

5.6

11-20 OSAT

+0.586

-0.145

18.7 0.46

+0.0044

8.0 0.20 +0.0054

3.1 0.08

+0.0094

2.9 0.05

+0.0166

2.3 0.05

+0.916

2.0 0.05 -0.063

1.4 0.06 +0.044

1.3 0.02

+3.65

1.9 0.04

Table 11-32. Coefficients, coef./s.d. ratios, and calculated contributions of independent variables associated with

durability, weight loss, and saturation ratio (Series A

concretes made of AE + NAE cements)

Column

Eq. No.

Table No. Dependent variable Constant

Air content, coef.. coef./s.d Calculated range. w/c, coef

coef./s.d.. -. Calculated range. C3A, coef

coef./s.d Calculated range.

C2S, coef

coef./s.d Calculated range. C4AF. coef

coef./s.d Calculated range. NajO, coef

coef./s.d CalciJated range. K2O, coef

coef./s.d Calculated range. MgO, coef

coef./s.d Calculated range. APF, coef

coef./s.d Calculated range. C3A/SO3, coef

coef./s.d Calculated range.

Loss, coef

coef./s.d Calculated range.

Ba, coef

coef./s.d Calculated range.

Co, coef

coef./s.d Calculated range. Cu, coef

coef./s.d Calculated range. Mn, coef. coef./s.d. Calculated range.

Ni, coef. coef./s.d Calculated range.

P, coef

coef./s.d Calculated range.

Pb, coef

coef./s.d Calculated range. Rb, coef

coef./s.d Calculated range

Ti, coef

coef./s.d Calculated range.

Zr, coef

coef./s.d Calculated range .

> (AAIR)»-5.

11-8 ADUR

+52.38

+7.82

18.4 78

-0.4679

3.9 21

-15.93

3.6 18 -2.378

3.2 12 -0.00297

1.8

-47.94

2.0 10

-232.0

2.5 12

-204.1 -52.54

1.6 1.3 10 2.6 -895.2 -329.2

1.9 2.2 9 3.3 -12.55 -4.379

1.4 2.0 13 4.4

11-16 AWTL

+1,157

+0.902

7.0 9.0

+0.5275

4.9

7.4

+0.6059

4.3

9.1 +2.527

1.6

1.8 -9.70

7.0

1.1

-4.903

2.3

4.9

26
Series 0 and Series A concretes respectively with

both air-entraining and non-air-entraining ce- ments included. The equations are presented

vertically instead of horizontally as in the previous

tables. Coef./s.d. ratios to indicate the probable

significance of the coefficients, and the calculated

ranges of the contributions of the different independent variables are also given.

Comparison of the coefficients in the three

columns of table 11-31 shows that higher air content was associated with all three of the dependent variables: durability factor, weight loss,

and saturation ratio. In each case the coef./s.d.

ratio was 10.0 or greater. Durability factor and

weight loss are related effects, since specimens

which remain in the freezing-and-thawing test longer, thus having higher durability factors, also

lose more weight by sloughing. Thus, all the independent variables that appear in both columns 1 and 2 have the same sign in both. The degree of saturation at the time freezing-and-thawing tests start has a significant effect on length of time in the freezing-and-thawing test, and thus on both

durability factor and weight loss. Note that all of the coefficients for independent variables that

appear in column 3 as well as in either 1 or 2, with

one exception, have opposite signs in column 3 to the ones in columns 1 and 2, indicating that

factors that are associated with a higher degree of saturation are associated with lower durability

and weight loss. Part of the correlation between

saturation and air content is due to the fact that

the percentage of air is included in the calculation

of the saturation ratio. The independent variables, other than air content, that showed a significant association with

two or more of the dependent variables in columns

1, 2, and 3, were C2S, C4AF, K2O, MgO, Cu, Rb,

and Ti, with possibly Na20 and Pb added.

Cements with high C2S, MgO, and Cu were

associated with concretes having high saturation

ratios and low durability factors. However, high

C4AF, which was associated with high saturation

ratio, was also associated with high weight loss but

showed no significant association with durability

factor. This suggests that, if these associations

result from real cause and effect relationships,

the mechanism by which C4AF affects the sat- uration ratio differs from that by which the

other independent variables affect it. Increasing

loss on ignition was also significantly associated

with increasing saturation ratio, but showed no

significant association with either durability factor

or weight loss. Increases in both the two alkalis

showed significant associations with decrease in weight loss, but neither had a significant relationship to saturation ratio, and only K2O had a

significant negative association with durability

factor. The coefficient for Na20 was negative, but

the coef./s.d. ratio was only 1.9. It is possible that

the apparent difference between the two alkalis is due to the wider range of values that existed for

K2O as compared to Na20 (1.1 percent compared

to 0.7 percent, respectively).

Experience in the laboratory and in the field has demonstrated repeatedly and conclusively

that if the objective is to produce concrete which

will resist damage from freezing and thawing, so

far as the paste is concerned, the easiest, cheapest,

and surest way to accomplish that end, assuming

the concrete is well-designed in other respects,

made with good materials, and properly cured, is by the incorporation in the concrete of an adequate system of entrained air voids [2, 5]. Previous

studies have indicated that, although changes in composition, fineness, or other properties of the

cement may cause significant changes in durability of non-air-entrained concretes, the increase

in durability produced by entrained air is so dramatic that the effects of properties of the

cement are overshadowed. There is nothing in the results of the present study that changes this

picture in any essential manner, although the data

do serve to round out some details, thanks mainly

to the large number of cements tested. One result

from this study is that indications are given of

what independent variables may be related to durability of non-air-entrained concretes and to what degree. No indications, unfortunately, are given as to possible relationships in air-entrained concretes directly, because of the small number

of air-entraining cements tested. The above conclusions are based on the following features of the results with the Series 0 concretes, with a nominal 53^ bags of cement per

cubic yard and a water-cement ratio of 0.635.

(Results with the A series with constant slump

are similar.)

Table 11-1 shows that all concretes made with

non-air-entraining cements had durability factors

less than 60, which means that they all suffered a

40-percent reduction in dynamic modulus in less than 300 cycles of freezing and thawing. All of the

concretes made with air-entraining cements, however, had durability factors greater than 60, and

required from about 300 to almost 1000 cycles of freezing and thawing to produce a 40-percent

reduction in dynamic E.

In table 11-3, for non-air-entrained cements

only, eq 1 relates only one independent variable,

air content of the concretes, to the durability

factor in the laboratory freezing-and-thawing test. The coefficient for air content is highly significant,

being about 33^9 times its estimated standard

deviation, and a significant reduction in the overall S.D. occurs, from 11.22 to 10.85. When six more independent variables are included in the

analysis (eq 3) a further significant decrease in S.D. occurs, and all of the added coefficients are

greater in magnitude than their s.d.'s, although

only three of them have coef./s.d. ratios greater

than or equal to 2. In eq 4 with five of the trace elements included as independent variables, a

further significant reduction in S.D. occurs; all of the added variables have coefficients gi-eater in

27
magnitude than their s.d.'s with three being

greater than two times the s.d.; and coef./s.d.

ratios for the previously included independent

variables are as great as or greater than the cor- responding ones in eq 3. Also, in going from eq 1 to eq 3 and then to eq 4, there is a progressive

increase in both coefficient and coef./s.d. ratio for

the air content. To summarize, although there was a significant relationship between the durability factor and air content for the non-airentraining cements, there was an additional

significant correlation with seven out of eleven

additional independent variables, after the correlation with air content was accounted for. Turning to table 11-2 where data for 12 air- entrained cements are included with the 168 nonair-entrained cements represented in table 11-4,

remarks similar to those given above apply to comparisons between eq 1, 3, and 4. However,

there are interesting differences between corre- sponding equations in the two tables. In the first place, the coefficients for air content in table 11-2

are larger than those in the corresponding equations in table 11-3, and their s.d.'s are smaller,

thus causing a large increase in coef./s.d. ratio. These ratios are 3.6, 5.2, and 6.4 for eq 1, 3, and 4,

respectively, in table 11-3; and 17., 20., and

21. for the corresponding equations in table 11-2.

This, of course, shows the large effect of entrained

air on durability. In general, however, the coeffi- cients and coef./s.d. ratios for the other independent variables in eq 3 and 4, table 11-2 are about the same as the corresponding ones in table

11-3, with the same ones being significant in both

cases. This may be explained by the fact that the

added data for the independent variables other

than air content were generally in the same range

for the twelve air-entraining cements as for the

non-air-entraining cements, while the values for

air content were much higher. However, it is of interest that, even with the increase in average

durability and in significance of the air content,

the other independent variables still show significant correlations. It is, of course, impossible from

the evidence given here to predict what would

happen if a much larger number of air-entraining

cements had been included, or if air-entraining

cements alone had been subjected to the same

type of analysis.

Statistically significant relationships, of course, do not in themselves constitute evidence of causeand-effect relationships between variables. It is well known from experimental evidence that en- trained air is a cause of increased durability, and

much research has gone into investigation of the

physical reasons for the effect. So far as the statistical correlations between durability and the

other independent variables discussed here are concerned, however, there is no such body of knowledge available. Whether or not any of the

relationships indicated are direct effects, or whether they have an indirect effect on durability

through their effect on some other variable, or

whether the indicated correlation is gratuitous, can not be determined positively. Two hypotheses

that appear plausible, however, and are capable

of some investigation on the basis of the data

obtained -.n this study, are that some of the independent variables other than air content may

affect durability indirectly through their effect on

the system of entrained air voids or through their

effect on the degree to which the concretes took

up water during the soaking period that pre- ceded freezing.

The equations shown in tables 11-33 through

11-36 were calculated to investigate these hypotheses further. These tables give results for the

0- and A-series concretes, with and without the

air-entraining cements. The seven equations in

each of the four tables all include the same set of independent variables as those in eq 4, tables

11-2 and 11-3. Also the same 177 cements are included in tables 11-33 and 11-34 and the same

165 cements in tables 11-35 and 11-36. Thus

comparisons may easily be made of the effects of using different dependent variables or of adding

air content, saturation ratio, or both as independent variables.

Equation 4 in all four tables shows the relationship of the basic set of eleven independent variables to durability factor of the concretes with no

other independent variables included. In the

equations with all cements (tables 11-33 and

11-34) the only independent variables which had

coef./s.d. ratios greater than 1.0 were C2S, Rb,

and Cu; and Rb was the only one whose ratio was greater than 2.0. For the non-air-entraining

cements only, there was a difference between the

series 0 concretes (table 11-35) and the series A

concretes (table 11-36). In the former, three of

the coef./s.d. ratios, C2S, K2O, and MgO, were

greater than 2.0, and four others were greater

than 1.0. In table 11-36 six coef./s.d. ratios were

greater than 1.0, but none was greater than 2.0. All of the coef./s.d. ratios that were greater than

1.0 in eq 4, table 11-35, decreased in table 11-36.

This indicates an effect of water-cement ratio

which will be discussed further below. Note that

all of the coefficients whose coef./s.d. ratios were

greater than 1.0 in each of the eqs 4 were negative,

indicating that increases in these variables were

related to decreases in durability factor.

7.2. Effect of Alkalis on Durability

Equations 1 and 2 in all four of the tables (11-33

through 11-36) show relationships between the same set of independent variables as those in eq 4

and air content and saturation ratio of the concretes, respectively. In eqs 1 for air content, the

coef./s.d. ratios for both NaeO and K2O are greater

than 2.0 in all cases. In fact, the coef./s.d. ratios

for K2O in all four cases and for Na20 with the

non-air-entraining cements were greater than 3.0. The coefficients are all positive also, indicating

that increases in the alkalis were significantly

related to increased air content.

28
Table 11-33. Relationship of durability factor, air content, and saturation ratio to various independent variables; 0 series concretes, air-entraining and non-air-entraining cements

Column 1 2 —

3 4 5 6 7 Dependent Variable OAIR OSAT OAIR ODUR ODUR ODUR ODUR

Constant -0.890 0.637 9.20 80.8 88.4 176. 111. Air content

8.52 7.02

s.d..._ " 0.422 0.667

20.2 10.5 Saturation ratio coef. _ — 15.8 -150. -38.4

s.d. 0 974 10 75 13.5

16.3 13.9 2!86 CiS

0.00236 -0.000954 -0.0128 -0.502 -0.522 0.645 -0.556

s.d. 0.0546 0.00271 0.0339 0.551 0.296 0.374 0 290

0.043 0.35 0.38 0.91 1.77 l!72 l!92 CzS —0.00461 0.00425 0.0627 -0.915 —0.876 -0.279 -0.719

s.d. 0.0502 0.00249 0.0314 0.506 0.272 0.347 0.272

0.092 1.71 2.00 1.81 3.22 o!80 2!65 Na20

coef 1.779 -0.0746 0.600 6.81 -8.34 -4.35 -8.54

s.d. 0.823 0.0408 0.516 8.30 4.52 5.69 4.42

2.16 1.83 1.16 0.82 1.85 0.76 1.93 K2O

2.51 -0.1070 0.818 1.31 -20.1 -14.7 -20.4

s.d. 0 787 0.0390 0.499 7.94 4.39 5.51 4.30

3.19 2.74 1.64 0.17 4.58 2.67 4^75 MgO

0.176 —0.000798 0.164 -0.807 -2.31 -0.927 -2.08

s.d. 0.133 0.00658 0.0824 1.34 0.723 0.909 0.712

1.33 0.12 1.99 0.60 3.20 1.02 2.92 APF

0.000265 -0.00000909 0.000121 -0.000702 -0.00296 -0.00206 -0.00291

s.d. 0.000286 0.0000143 0.000178 0.00289 0.00155 0.00196 0 00152

coef./s.d. o!93 0.64 0.68 0.24 l!90 1.05 1.91 Ba

1.038 -0.0363 0.463 —28.2 -37.0 —33.6 -36.8

s.d. 4.15 0.206 2.58 41.8 22.5 28.4 22.0

0.25 0.18 0.18 0.67 1.64 1.18 1.67 Rb — 168. 1.063 -151. -2416. -984. -2257. -1195.

s.d. 79.2 3.93 49.2 799. 435. 543. 432.

coef./s.d. 2!l2 o!27 3!08 3.02 2^26 4!l6 2!77 Pb

5.07 —0.387 — 1.063 -171. -214. —229. —221.

s.d. 22.4 1.109 13.9 225. 121 153. 119

o!23 o!35 0!077 0.76 1.77 1.49 l!87

Ti

1.46 -0.0711 0.335 0.936 — 11.50 —9.70 -12.0

s.d 1.17 0.0580 0.729 11.79 6.36 8.05 6.23 1.25 1 23 0.46 0 079 1.81 1.21 1.93 Cu

coef. . -4.10 1.135 13.9 -229. -194. -58.7 -156.

s.d 16.1 0.796 10.02 162. 87.0 111. 86.1

coef./s.d 0.26 1.43 1.38 1.41 2.23 0.53 1.81

The question arises, if increased alkali content was associated with increased air content, why

was it not also associated with a higher durability

factor? Looking at the coefficients for the two

alkalis in eq 2 in all four tables, we find that all eight of the coef./s.d. ratios were greater than 1.0, and all but three of these were greater than 2.0. The coefficients, however, are all negative, indicating that a decrease in saturation ratio was

associated with increases in alkali content. This

again might be expected to indicate that increases

in alkali content should be associated with in- creased durability. In eq 3 with air content as the dependent variable and saturation ratio included as an independent variable, the coef./s.d. ratios for the

alkalis are consistently reduced and remain significant only for the non-air-entrained cements.

Comparing eq 4, in which durability factor is related only to the basic set of 11 independent

variables, with eq 5, 6, and 7, in which air content

alone, saturation ratio alone, and both together

are included as independent variables, shows that

whatever relationship existed between the basic

independent variables in these equations and

durability was influenced by their relationship

with air content and saturation ratio. Of the 148

coefficients for independent variables (not counting the constant terms) in eqs 5, 6, and 7, only six had coef./s.d. ratios less than 1.0, but 66, or about

45 percent had coef./s.d. ratios greater than 2.0. For the alkalis specifically, note that in eq 4

29
Table 11-34. Relationship of durability factor, air content and saturation ratio to various independent variables; A series concretes, air-entraining and non-air-entraining cements

Column 1 2 3 4 5 6 7

Dependent variable AAIR ASAT AAIR ADUR ADUR ADUR ADUR

Constant -3.91 -0.845 10.59 60.1 88.2 180. 135.

Air content

7.17 4.25 0.431 0.778

16.6 5.47

Saturation ratio

coef. . . - -17.2 -142. -69.1

a A 0 827 8.93 15.7

coef./s.d _ 20;8 15.9 4!40

CaS

0.0249 -0.00254 -0.0188 -0.249 -0.427 -0.610 -0.530

CI A 0.0618 U.UUoUD 0.326 0.559 0.342 0.352 0.325

coef./s.d 0.40 0.83 o!58 o!45 l!25 l!73 l!63

C2S

coef 0.0298 0.00224 0.0683 -0.682 -0.896 -0.364 -0.654

a A 0.0568 A AQAA 0 514 0 314 0 324 0.303

0.53 0.80 2.28 l!33 2^85 i;i2 2!l6 NaiO

coef 1.87 -0.130 -0.344 5.77 -7.62 -12.5 -11.08

a A 0.501 8.41 5.21 5.42 5.00 2.01 2.79 o!69 o!69 l!46 2!32 2^22 K2O

coef.-. . . 2.98 -0.162 0.196 1.90 -19.5 -21.1 -22.0

A 0.890 0.0441 0 487 8.05 5.09 5.26 4.86

3.35 3.68 o!40 o!24 3!83 4!o2 4!53 MgO

0.262 -0.00318 0.207 -0.306 -2.18 -0.758 -1.64

0 A 0.150 U.UU / 44 0 0791 1 36 0.838 0.854 0.804

coef./s.d 1.74 0.43 2!62 o!23 2]61 o!89 2^04 APP

0.000377 -0.0000133 0.000149 -0.000381 -0.00309 -0.00227 -0.00290

a A A AAAA1 fiA A AAA1 71 A AAOQQ 0 001 80 nU. 001 vU A 84C* 0 001 70

1.17 0.83 0.88 0.13 1.72 1.23 1.70 Ba

2.88 -0.288 -2.06 -20.4 -41.1 -61.3 -52.5

o A 2 48 42 4 26 0 26.8 24.8

0.61 1.24 o!83 o!48 l!58 2^29 2!l2 Rb

-184. 0.915 -168. -224r. -925. -2111. -1397.

a A QQ fl 4.44 A'7 9 oXU. 502 510 488. 2.05 0.21 3.56 2.77 1^84 4!l4 2^86 Pb

11.7 -1.153 -8.09 -106.2 -190. -270. -236.

0 A 25.3 1.25 1 <1 Q 99Q 14U. 144 133. 0.46 0.92 0.61 0.46 1.36 l!87 l!77

Ti

2.09 -0.1172 0.0825 3.88 -11.18 -12.8 -13.1

s.d 1.32 0.0656 0.703 11.96 7.37 7.59 7.00

1.58 1.79 0.12 0.32 1.15 1.68 1.87 Cu

-7.08 0.768 6.10 -275. -225. -166. -192.

s.d 18.2 0.900 9.58 164. 100.4 103.5 95.5

coef./s.d. 0.39 0.85 0.64 1.68 2.24 1.16 2.01

only one of the eight coef./s.d. ratios is greater

than 2.0, and only two others greater than 1.0. However, in eqs 5, 6, and 7 in the four tables, 22 of the 24 coefficients for the two alkalis are greater

than 1.0 and 14 of these are greater than 2.0. It has been established by research over a number of years that the beneficial effect of en- trained air on the durability of concrete depends

not only on the amount of air present, but also on the character of the distribution of that air throughout the paste matrix [16, 17, 18, 19]. For

the air to be effective in preventing the build-up

of pressures which can cause disruption of the

paste during freezing, a significantly large proportion of the total volume of air needs to be present

in the form of small discrete bubbles, evenly distributed throughout the paste. Two parameters of the air void system in the hardened concrete which are of importance in relation to the efficacy

of that system in providing protection from frost damage are: (1) the specific surface, a, which is a measure of the ratio of total surface area of the

voids to their total volume, and (2) spacing factor,

L, which is a measure of the average distance

between adjacent bubbles in the paste, and thus

of the average distance water has to travel in the

paste to a bubble where it can freeze without

causing trouble. Large a and small L are related

to better frost resistance of the concrete. The results of studies by Mielenz and others

30
Table 11-35. Relationship of durability factor, air content, and saturation ratio to various independent variables; 0 series concretes, non-air-entraining cements.

Column 1 2 3 4 5 6 7 Dependent variable OAIR OSAT OAIR ODUR ODUR ODUR ODUR

Constant -1.59 0.638 2.62 80.2 91.4 129. 119. Air content

7.00 3.74

s.d 1.10 1.39

coef./s.d 6.36 2.69

Saturation ratio coef -6.61 -76.4 -51.8

U.D04 11.07 14.2

10.4 6.91 3.65 CS

coef. . 0.0267 -0.00153 0.0166 -0.343 -0.530 -0.461 -0.523

0.0224 ft ftftOI

0

A ftl TO ft Q/*9 0.306 0.300 0.295

coef./s.d . . . 1.20 0.70 0.97 1.004 1.73 1.54 1.77 C2S

0.01104 0.00391 0.0368 -0.777 -0.854 -0.478 -0.616

« A 0.021 ft ftftOftI 0.0159 U.Oi4 0.280 0.278 0.277

coef./s.d . . 0.54 1.95 2.31 2.48 3.05 1.72 2.22 NajO

1.056 -0.0495 0.729 0.412 -6.98 -3.37 -6.10

n A 0.331 ft ftOOO 0.255 5.06 4.66 4.46 4.48

3.19 1.53 2.85 0.082 1.50 0.76 1.36 K2O

1.114 -0.0614 0.708 -10.44 . -18.2 -15.1 -17.8

a A 0.324 0.0317 ft OK1 4.58 4.39 4.41 3.44 1.94 2.82 2.11 3.98 3.45 4.03 MgO

0.0478 0.00357 0.0714 -2.13 -2.46 -1.85 -2.12

a A 0.0544 ft ftftKQO 0.0418 ft 8*59 0.744 0.729 0.721

0.88 0.67 1.71 2.55 3.31 2.54 2.94 APF

0.000115 -0.00000169 0.000104 -0.00265 -0.00346 -0.00278 -0.00317

a A ft Aftfti 1 T ft ftftftm 1 A ft ftftftftUQK ft ftfti "TO U.UUlDU A /\A1 0.00156 0.00154

0.99 0.15 1.16 1.48 2.16 1.78 2.06 Ba

2.78 -0.109 2.06 -16.6 -36.0 -24.9 -32.6

A 1.65 0.161 25.2 22.7 22,1 21.8

1.69 0.68 1.63 0.66 1.59 1.13 1.50 Rb

45.7 -6.01 6.01 -590. -910. -1050. -1072.

a A 32.4 3.16 OK 1 494. 444. 438. 429.

1.41 1.90 0.24 1.19 2.05 2.40 2.50 Pb

7.21 -0.469 4.11 -149. -199. -184. -200.

0 A 8.85 0.864 6.79 135. 121. 118. 116. 0.81 0.54 0.61 1.10 1.65 1.56 1.72

Ti

0.915 -0.0553 0.550 -5.89 -12.3 -10.1 -12.2

s.d 0.479 0.0468 0.369 7.82 6.60 6.43 6.35

1.91 1.18 1.49 0.81 1.86 1.57 1.92 Cu

15.4 0.440 18.3 -62.1 -170. -28.5 -96.9

s.d 6.40 0.625 4.92 97.9 88.9 85.8 87.8

2.41 0.70 3.72 0.63 1.91 0.33 1.10

[20] on the mechanisms by which air-entraining

agents facihtate the production of an efficacious

air void system in hardened concrete, provide

possible explanations for some of the trends shown

by these data. In plastic concrete, the air in smaller voids, which are those mainly responsible

I for the increased durability of air-entrained concrete, is under greater pressure than that in larger

voids. The tendency is for air in the smaller voids

to dissolve in the water in the mix until the latter becomes saturated and then for air to be released

from the solution into larger voids which are under

lower pressure [21]. Thus, while the concrete is

still plastic, larger air bubbles tend to grow at the

expense of smaller bubbles producing an increase

in total air content (providing too many of the

large bubbles do not escape from the surface), a

decrease in specific surface a of the air void sys- tem, and an increase in the spacing factor L. The

effect of a good air-entraining agent is to change

conditions at the air-water interface in such a way

as to decrease the rate of transfer of air from

smaller bubbles to larger ones, and thus to pre- serve the system of smaller bubbles which is effective in producing increased frost resistance.

Mielenz, et al, [20] show that certain constitu- ents that may be introduced by the cement and

certain characteristics of the concrete mixes or

their handling prior to hardening, have an effect on the operation of air-entraining agents. Their

31
Table 11-36. Relationship of durability factor, air content, and saturation ratio to various independent variables; A series concretes, non-air-entraining cements

Column 1 2 3 4 5 6 7 Dependent variable AAIR ASAT AAIR ADUR ADUR ADUR ADUR

Constant -3.94 0.825 3.28 68.7 97.1 142. 136.

Air content

7.19 1.87

s.d 1.04 1.65

6.92 1.14

Saturation ratio coef -8.75 -89.1 -72.7

a 0.533 10.9 1 ft 1 16^4 8!21 4.03 C3S

ciief S.u. 0.0444

1.74

-0.00301

A AA9QQ

1.29

0.0181 0.0154

l!l7

-0.213

0.374

o!57

-0.532

0 331

1.61

-0.481

0 314

l!53

-0.515

0.315

1.63 C2S

coef. .

r. A 0.0348

0.0234

1.49

0.00211

A AA91

Q

0.99

0.0533

0 0141

3.77

-0.631

0 343

l!84

-0.881

0 302

2;9i

-0.443

0.287

1.54

-0.543

0.300

1.81 NaaO

a A S.C1._- 1.170

U.O i 0 3.11

-0.103

0.0344

2.99

0.270

0.233

l!l6

0.439 5 53

o!79

-7.97

4 99

l!60

-8.73

t. to 1.84

-9.23

4.77

1.94

coef A

coef./s.d

1.42 0 369

3!84

-0.105

A AQQ*? U.UOO ( 3.10

0.500

0 229

2!l8

-9.03

5 42

1.67

-19.2

4 96

3!87

-18.4

4 66

3!93

-19.3

4.73 4.08 MgO

0 A 0.0992

A Afil Q U.UDiy

1.60

0.00282

U.UUOOO

0.50

0.124

0 0373

3!32

-1.81

0 910

1^99

-2.52

0 803

3.'l4

-1.56

2.05

-1.79

0.787

2.28 APF

coef.-. - n A S.d. 0.000211

A AAAI QQ

1.59

-0.00000460

A AAAA1 0

1

0.38

0.000171

fl AAAAftAI 2.14

-0.00243

A AA1 Qc: 1.25

-0.00395

A AA1 2.29

-0.00284

A AA1 CO

1.74

-0.00316

A AA1 a C 1.91 Ba

coef. _ a A S.U. 4.88

1 (17 2.60

-0.374

0.171

2.18

1.61

1 15

l!40

-9.40

27 5 o;34

-44.5

OA R

1.81

-42.7

1.83

-45.7

23.5

1.95 Kb

s.d 49.7

36.8

1.35

-7.70

3.36

2.29

-17.7

22.6

0.78

-560.

541.1.04

-918.

476.

1.93

-1247.

459.

2.71

-1214.

460.2.65 Pb

coef.

a A

15.0 10.07

1.49

-1.28

0.920

1.39

3.78

1 A 0.62

-75.4

0.51

-183.

130.1.41

-190.

124.

1.53

-197.

124.1.58

Ti

s.d 1.35 0.545

2.48

-0.0921

0.0498

1.85

0.547

0.332

1.65

-4.38

8.00 0.55

-14.1

7.14

1.98

-12.6

6.76

1.86

-13.6

6.81 2.00 Cu

coef...

s.d coef./s.d

15.3 7.29 2.10-0.0561

0.666

0.084

14.8

4.39 3.37

-123.

107.1.15

-232.

95.0 2.45

-128.

89.4

1.43

-155.

92.6

1.68

work was done mainly on neat cement slurries

and pastes to which air-entraining agents had

been added, while the work reported here was

done on concretes most of which were made with

non-air-entraining cements. However, the fact

that many of the effects detected with our data

are compatible with the explanations given by

Mielenz, et al., and these comparisons tend to be

reinforced when the twelve air-entraining cements

are included in the analysis appears to be worthy

of consideration. There are substances which may

accidentally or purposefully (such as grinding

aids) become incorporated in a non-air-entraining

cement which may act to some extent as air- entraining agents, and if such substances are

present, then the effects shown in Mielenz work

might explain some of our indicated relationships.

Unfortunately measurements on the air-void sys- tems in the hardened concretes are not available

at the present time to provide a further check on

possible conclusions, but the indicated trends are explored here. In the Bureau of Reclamation work [22] some

mixtures were prepared with NaOH added. It was known that Na+ and K+ ions had a depressing

effect on calcium in solution, and it was therefore

postulated that sodium would have an adverse

effect on the action of air-entraining agents which

produced a film composed of the calcium salt of the surface active constituent of the agent. The

32
result of the addition was that L increased and a

decreased compared to those obtained with similar

mixes with the same w/c ratio and without the

added alkali. In Mielenz' slurries the total air content measured by the air meter remained constant when the alkali was added, while in our

data, air content consistently increased with

increased alkali. This could be explained by the

hypothesis that in the neat cement mixture the

large voids present and produced by coalescence

of smaller ones could escape more easily, while in concrete mixtures, the large voids tend more to be retained by adhesion to or entrapment in the

aggregate particles. Thus the negative association

between durability factor and alkalis shown in our

concrete data in spite of the positive association

between air content and alkali, could be explained

by the hypothesis that dissolution of small bubbles

and growth of the large ones took place.

7.3. Saturation Ratio

Explanations of the negative associations of saturation ratios with the alkalis are more doubtful. It seems reasonable to assume that if alkalis

have some effect on the size, closeness together,

and possible interconnections of the air voids in the concrete, they would also have some effect on

the rate at and extent to which the concrete could

soak up water. However, the fact that coefficients for the alkalis are negative in equations in which

the saturation ratio is the independent variable

while they are positive in relation to air content

could be largely due to the circumstance that air content is a factor in the denominator of the

formula for calculating saturation ratio.

7.4. Water-Cement Ratio

Water-cement ratio is another factor which is

j shown by Mielenz to have an effect on the rate of dissolution of small voids and thus on spacing

factor, specific surface, and durability [23, 24].

I Increased water/cement ratio tends to increase

j the fluidity of the mixture, thus aiding the dissolution of small bubbles aijd decreasing frost re- sistance. Comparisons between equations in table

i 11-33 and 11-35 for constant w/c concretes with

i corresponding ones in tables 11-34 and 11-36

where w/c varied, are somewhat inconclusive, but

i there are some differences which may be of

interest. For instance, comparing eqs 4 in tables

11-35 and 11-36, shows that for all of the independent variables except one, the coef./s.d. ratios

in table 11-35 are larger than those in table 11-36.

This would indicate that permitting the w/c to vary increased the variation in durability factor

and thus reduced the significance of the other

variables in the equation when this extra variation was not accounted for. In order to check this

further, some additional equations, not presented

here, were calculated using w/c ratio of the Aseries concretes as a dependent variable with the

following results: Water-cement ratio (at constant slump)

a. had a negative relationship to air content;

b. had a positive relationship to saturation

ratio;

c. had a negative relationship with durability

factor when all cements were included, but was not significant when the air-entraining

cements were excluded.

As Dr. Mielenz observed in a private communication, item c above "is extremely important since

it shows the significance of w/c even when concrete is purposefully air-entrained. One explanation is the decreasing value of alpha as w/c

increases."

7.5. Slump

According to Mielenz [25] decreased slump decreases average void size. Additional equations

calculated from our data using the slump of the

constant w/c ratio concretes indicated the fol- lowing:

Slump (at constant w/c ratio):

a. had a positive relationship with air content;

b. had a negative relationship with saturation

ratio when all cements were included, but was not significant when air-entraining

cements were included;

c. had a positive relationship with durability

factor. The picture here is somewhat confused. Mielenz'

tests showed that the effect of slump on durability

factor was different with different types of air- entraining agents [26]. With our data, there is no

information as to what kind of substance, if any, was acting as an air-entraining agent in the nonair-entraining cements, nor even what types were

present in the air-entraining cements. As Mielenz

pointed out in the private communication mentioned above, "the correlations that are forthcoming from my tests (Series II in ref. [23]) are not subject to the same interpretation as are your

data because my tests compare the effect of slump

on given cement-AEA combinations whereas yours

evaluate the effect of slump on concretes containing diverse cements, the variation in slump occurring at constant w/c. In other words, the concretes developing high slump in your tests contain ce- ments of proportionately lower water requirement,

in part because they are air entraining."

In spite of the complications, in view of all the

evidence, it seems reasonable to suspect that

whatever effect slump has on air content and

durability may be largely due to an effect of some

kind on the character of the air void system.

33
7.6. Setting Time

The last variable for which there is any basis

for comparing our findings with those of Mielenz

is setting time. He points out that anything that

prolongs the time of setting increases the time

available for dissolution of smaller bubbles before

hardening takes place, and therefore results in lower specific surface and higher spacing factor

[27]. Mielenz' work was done on neat cement

mixtures with retarders added to prolong setting

time, whereas in our tests on concretes, only the

results of normal variation in setting time of the

cements were available. No tests of setting time

of the concretes were made. However, additional

equations calculated with setting time of the

cements as an independent variable produced the

following results:

a. both initial and final set had a significant

positive relationship with air content when all cements were included, but not when the air- entraining cements were excluded;

b. both initial and final set had a significant

positive relationship to saturation ratio with only

non-air-entraining cements; and final set had a

significant positive relationship when all air- entraining cements were included;

c. both initial and final set had significant

positive relationships with durability factor when

saturation ratio was also included as an independent variable, both with all cements and with

air-entraining cements excluded.

Mielenz had the following to say on these results, "The correlation involving setting time of

the cements indicates that this property influences

the various qualities of the concrete directly or

indirectly. A time-of-setting test on the matrix of concrete would be more meaningful. Your correlation of set with air content (a, above) suggests

that air content of AE concrete increases with

setting time of air-entraining cement, but possibly

the relationship is due to a tendency of the AE

addition to increase setting time of the cement,

rather than through any direct action of setting

time on the air content of concrete." So far as the remaining independent variables

in the equations in tables 11-33, 11-34, 11-35,

and 11-36 are concerned, we are not aware of any

other work with which our results might be compared. Air permeability fineness appears to have

a negative association with durability factor for

the non-air-entraining cements only when air content is also included as an independent variable. MgO also shows significant negative association with durability factor when air content is included, both with and without the air-entraining

cements. Of the trace elements the only one which

shows a consistent significant relationship with

15.0

^ 12.0 o

tiJ z

ou

= 6.0-

z

0 3 0 <

6.0 12.0 18.0 24.0

AIR CONTENT 1:4 MORTAR, PERCENT

30.0

Figure 1. Results of plotting the air content of Series O concretes made with AE + NAE cements

versus the air content of 1 (cement to 20-30 Ottawa sand) mortars.

34
durability factor is rubidium. This association is most consistent when saturation ratio is included

as an independent variable.

When one considers the small amounts in which

rubidium and other trace elements are present in the cement, it seems unreasonable that they

should have an effect on such a gross property of the concretes in which the cements are incorporated as the number of cycles of freezing-andthawing the concrete specimens can withstand. If Rb, for instance, does have a real effect, it seems

that it would probably come about by means of some such mechanism as an effect on the most

finely divided portion of air void system such as those shown by Mielenz and his colleagues. Effects

of some of the trace elements should be investigated directly with neat cement mixtures using

similar techniques.

It is interesting to note that for all the independent variables except air content in eqs 4, 5, 6, and 7 in tables 11-33 through 11-36 that have

coef./s.d. ratios greater than 1.0, the coefficients are negative. This tends to indicate that, if the

hypothesis that the effect on durability is due to an effect on the films protecting the small air voids is valid, most of the minor ingredients that

have an effect have an adverse effect on the air void system.

7.7. Air Content of Test Mortars Versus Air

Content of Concretes

The relationship between the air in the Series 0

concrete (made with a w/c of 0.635) and the air

in the standard 1 :4 (cement to 20-30 Ottawa sand)

mortar is presented in figure 1. This graph is a

plot of the values of both the AE and the NAE

cements. Some of the plotted points represent more than one value because of the limitations of the computer printer when used as a plotter. A

corresponding plot of the air contents of Series A

concretes (5 + 1-in slump) versus the air content

of the 1:4 mortars, both made of AE + NAE

cements, is presented in figure 2. In both figures

1 and 2, the cements having high air content in the 1:4 mortar also had high air content in the

concrete. The Series 0 concretes appeared to have

a smaller dispersion of values.

Using different scales, plots were also made of the relationships of air in concrete and air in mortar made of the NAE cements. These plots are presented in figures 3 and 4 for the Series 0

and A concretes respectively.

The equations calculated for the relationships

between the air content of the 1:4 (cement to 20-30 Ottawa sand) mortars (SAIR) and the air

15.0 -

uj 12.0 o

ITUJ

a.

UJH

UJg 9.0 z

oo

CO

UJ 6.0

UJ<n

I-z

UJz

oo

<

3.0 -

6.0 12.0 18.0 24.0 AIR CONTENT 1:4 MORTAR, PERCENT

30.0

Figure 2. Results of plaiting the air content of Series A concretes made with AE + NAE cements

versus the air content of 1 {cement to 20-30 Ottawa sand) mortars.

35
content of the Series 0 and A concretes made of AE + NAE, and the NAE cements are presented

in table 11-37. The reduction of variance ("F"

values) was, in each equation, highly significant.

However, when the AE cements were included as

in eqs 1 and 2 the "F" values were about 10 times

those of eqs 3 and 4 where only the NAE cements

were included.

Table 11-37. Relationship of air-contents of concretes OAIR and AAIR, and the air-contents of 1:^. (cement to 20-30 Ottawa

sand) mortars, SAIR

Equation No.

Figure No. Cement

type

OAIR = -1.604 + 0.455 SAIR

s.d. (0.114) (0.013) AAIR = -2.103 + 0.560 SAIR

s.d. (0.145) (0.016) OAIR = -0.388 + 0.274 SAIR

s.d. (0.178) (0.024) AAIR = -0.703 + 0.307 SAIR

s.d. (0.214) (0.029)

"F" D.F.

Critical F

638 2:189 3.05

488 2:189 3.05

66 2:175 3.05

57 2:175 3.05

AE +NAE

AE+NAE

NAE

NAE

HI

UJ

a.uT

IUJ

a:o

§ 3 o

o

w

LJ

o:UJ 9

(O '

1-z

UJo

o

0^<

I -

0- 6 9 12 AIR CONTENT i:4 MORTAR, PERCENT.

15

Figure 3. Results of plotting the air content of Series O concretes made with NAE cements versus

the air content of 1.% (cement to 20-30 Ottawa sand) mortars.

36
8. Summary and Conclusions

8.1. Laboratory freezing-and-thawing tests were conducted on concretes made of 199 portland

cements of different types and from different sources. One series of concretes was made using a water/cement ratio of 0.635 and the other series with the quantity of water adjusted to give a

5 ± 1-in slump. A nominal quantity of 5.5 bags

of cement per cubic yard was used. The 3- X 4- X 16-in specimens were moist cured for 14 days

then air dried for 28 days after which the rapid

(2 hr) cycles of freezing and thawing in water were started. The durability factor was calculated

from the relative dynamic Youngs' modulus of

elasticity, on the basis of 40-percent reduction or 300 cycles depending on which occurred first. The

freezing-and-thawing cycles were continued until a 40-percent reduction in modulus was attained

with all specimens. The specimens were then

placed in a fog room for different periods and

determinations made of the increase in fundamental resonant frequency in order to determine

the extent of autogenous healing.

8.2. The saturation ratio or amount of water

absorbed in 24 hours divided by the possible absorption ranged from 0.20 to more than 0.80.

8.3. The durability factor for the concretes which had been dried in laboratory air for 28 days

following moist air curing for 14 days ranged from

about 5 to 95 when frozen and thawed in water.

8.4. The concretes made with non-air-entraining cements withstood from 10 to about 300 cycles

of freezing and thawing before the dynamic modulus was reduced to 60 percent of that at the start

of the tests. The average number of cycles was

about 100. The concretes made of the air-entraining cements required about 300 to 900 cycles of

freezing and thawing for a reduction of 40 percent

in dynamic modulus.

8.5. At the time the concrete specimens had

attained a 40-percent reduction in dynamic modulus there was a weight loss ranging up to 22

percent. A few specimens which failed very early

had a slight weight gain.

8.6. After the freezing-and-thawing tests had

been continued until there was a 40-percent loss of dynamic modulus the concrete specimens were

stored in a fog room and retested after 1, 2, 3, 4, or 5 years. The non-air-entrained concretes generally regained their original dynamic modulus or more, but the air-entrained specimens did not

gain as much. All of the regain of dynamic modulus took place in 16 months or less. There were

significant differences between cements in amount

of autogenous healing.

5 -

UJ 4 o

q:

UJ

t-UJ

°^ 3 o

o

CO

UJE 2

Ul

(0

o ' <

6 9

AIR CONTENT 1:4 MORTAR, PERCENT.

12 IS

Figure 4. Results of plotting the air content of Series A concretes made with NAE cements versus

the air content of 1 .-^ (cement to 20-30 Ottawa sand) mortars.

37
8.7. Computations of multivariable equations

by a least-squares method were used to determine

the chemical and physical properties associated

with the durability factor, weight-loss at 40-per- cent reduction of dynamic modulus, and saturation ratio. The equations were computed for concretes made from all cements for which minor

constituents and trace elements had been determined. The equations were computed using as independent variables either the major potential

compounds or the major oxides, each with other

commonly determined variables, and these with

trace elements found to be significant.

The following observations relate to equations

as summarized in tables 11-31 and 11-32 for concretes made of AE + NAE cements using a water/cement ratio of 0.635 and concretes made

having a slump of 5 + 1 in. 8.7.1. The durability factor was primarily dependent on the air content of the concretes. Increases in CoS, KoO, MgO and possibly Cu,

Rb, Ti and fineness were associated with decreases

of the durability factor.

8.7.2. An increase of the air content was asso- ciated with an increase of the weight-loss at the

time of 40-percent reduction of dynamic modulus.

Increases of C3A and C4AF were also associated

with increases of the weight-loss. Increases in K2O and possibly Na^O, Pb, Rb, and Ti were

associated with decreases of the weight-loss.

8.7.3. An increase of the air-content was asso- ciated with a decrease of the saturation ratio. An

increase of the CoS, C4AF and possibly MgO, loss

on ignition, Rb, Ni, Co, and Cu were associated

with an increase of the saturation ratio.

8.8. Computations of multivariable equations

for the concretes made with non-air-entraining

cements were in general agreement with those

calculated with all the cements. The coefficients for the air content of the concretes were generally

not so highly significant as when the air-entraining

cements were included but they were generally

significant.

8.9. Computations made using the principal

oxides together with other commonly determined

variables, or these with minor constituents and

trace elements resulted in equations with nearly

the same estimated standard deviation values as when the calculated major potential compounds

were used as independent variables.

8.10. The coefficients for the individual trace elements were generally not highly significant

when used in multivariable equations for some of the dependent variables and their use did not

always result in a significantly better fit, i.e., a

significantly lower estimated standard deviation.

8.11. There was a good correlation between

the air entrained in the concrete and that en- trained in the standard 1:4 (cement to 20-30

Ottawa sand) mortar.

8.12. There was evidence that some of the

variables such as alkali, water/cement ratio,

slump, and possibly setting time, might have

influenced durability through an effect on the

air-void system, particularly the small air voids, as reported by Mielenz and others.

9. References

[1] Bogue, R. H., The Chemistry of Portland Cements,

2nd Edition, p. 716, Reinhold Publishing Corp. N. Y. (1955).

[2] McMillan, F. R., Tyler, I. L., Hansen, W. C, Lerch,

Wm., Ford, C. I,., and Brown, L. S., Bulletin 26, Research and Development Laboratories of the Portland Cement Association, Chicago, 111. (1948). McMillan, F. R., Stanton, T. E., Tyler, I. L., and

Hansen, W. C, Bulletin 30, Research and Development Laboratories of the Portland Cement Association, Chicago, 111. (1949). Verbeck, G. J. and Foster, C. W., Bulletin 32, Research

and Development Laboratories of the Portland Cement Association, Chicago, 111. (1949). Jackson, F. H. and Tyler, I. L., Bulletin 38, Research

and Development Laboratories of the Portland Cement Association, Chicago, 111. (1951).

[3] Grieb, W. E., and Werner, George, Natural Weathering of Concrete Specimens Prepared with Cements

used in the Long-Time Study, Public Roads 33, No. 4 p. o7 vOll. I96i).

[4] Mather, Bryant, Cement Performance in Concrete, Technical Report 6-787, U. S. Army Engineer,

Waterways Experiment Station, Corps of Engineers,

Vicksburg, Miss. (1967).

[5] Oleson, C. C, and Verbeck, George, Long-Time Study

of Cement Performance in Concrete, Chapter 8, Illinois Test Plot, Bulletin 217, Research and

Development Laboratories of the Portland Cement

Association, Skokie, 111. (1968).

[6] Standard Method of Test for Resistance of Concrete Specimens to Rapid Freezing and Thawing in Water ASTM Designation C290-67 or Resistance of Concrete Specimens to Rapid Freezing in Air and

Thawing in Water ASTM Designation C291-67.

[7] Arni, H. T., Resistance to Weathering, Significance

of Tests and Properties of Concrete and Concrete- Making Materials, ASTM STP 169 A (1966) pp. 261-274.

[8] Hornibrook, F. B., Discussion on paper by F. V.

Reagel, "Freezing and Thawing Tests of Concrete",

Proc. Highway Research Board 20 p. 598 (1940), see also "Progress Report Committee on Durability

of Concrete", Proc. Highway Research Board 24,

p. 175 (1944).

[9] Interrelations Between Cement and Concrete Properties, Part 1 —Section 1, Materials and techniques,

Blaine, R. L., Arni, H. T., and Foster, B. E.; Section

2, Water requirements of portland cements, Blaine, R. L., Arni, H. T., and Clevenger, R. A.; Section 3, Occurrence of minor and trace elements in portland

cements, Blaine, R. L., Bean, Leonard, and Hubbard, Elizabeth, K.; Nat. Bur. Stand. (U.S.), Bldg.

Sci. Ser. 2, 40 pages (Aug. 1965).

[10] Interrelations Between Cement and Concrete Properties., Part 2—Section 4, Variables associated with expansion in the potential sulfate exyraision test, Blaine, R. L., Arni, H. T., and Evans, D. NT;

Section 5, Heat of hydration of poriland cements,

Blaine, R. L., and Arni, H. Section 6, Variables

associated with small autoclave expansion values of Portland cements, Blaine, R. L., and Arni, H. T.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 5, 46 pages

(July 1966).

[11] Interrelations Between Cement and Concrete Properties, Part 3—Section 7, Compressive strength of mortars, Blaine, R. L., Arni, H. T., and DeFore,

M. R.; Section 8, Compressive strength of steamcured Portland cement mortars, Blaine, R. L., Arni,

38
H. T., and DeFore, M. R.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 8, 101 pages (Apr. 1968).

[12] Interrelations Between Cement and Concrete Properties, Part 4—Section 9, Shrinkage of hardened

Portland cement pastes, Blaine, R. L., Arni, H. T., and Evans, D. N.; Section 10, Shrinkage and expansion of concretes, Blaine, R. L., and Arni, H. T.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 15, 78 pages (Mar. 1969).

[13] Standard Method of Making and Curing Concrete Compression and Flexure Test Specimens in the Laboratory, ASTM Designation CI 92-66.

[14] Standard Method of Test for Fundamental Transverse,

Longitudinal, and Torsional Frequencies of Concrete

Specimens, ASTM Designation C215-60.

[15] Standard Method of Test for Resistance of Concrete Specimens to Rapid Freezing and Thawing in Water, ASTM Designation C290-67.

[16] Powers, T. C, "The Air Requirement of Frost Resist- ant Concrete," Proceedings, Highway Research

Board, Vol. 29, 1949, pp. 184-202.

[17] Powers, T. C. and R. A. Helmuth, "Theory of Volume

Changes in Hardened Portland Cement Paste During Freezing," Proceedings, Highway Research

Board, Vol. 32, 1953, p. 286.

[18] Kennedy, T. B. and K. Mather, "Correlation between

Laboratory Accelerated Freezing and Thawing and

Weathering at Treat Island, Maine," Proc. American

Concrete Inst., Vol. 50, 1954, pp. 141-172.

|19] Nerenst, P., "Frost Action in Concrete," Chemi.stry

of Cement, Proc. Fourth International Symposium

on the Chemistry of Cement, Monograph 43, Bureau

of Standard.s, 1960, pp. 807-828.

120] Mielenz, R. C, V. E. Wolkodoff, J. E. Backstrom, H. L. Flack, and R. W. Burrows," Origin, Evolution,

and Effects of the Air Void System in Concrete," Part 1 —Entrained Air in Unhardened Concrete, Journal ACI, Vol. 30, No. 1, July 1958, pp. 95 122; Part 2 —Influence of Type and Amount of Air- Entraining Agent, J. Am. Concrete Inst., Vol. 30, No. 2, Aug. 1958, pp. 261-272; Part 3—Influence of Water-Cement Ratio and Compaction, J. Am. Concrete Inst., Vol. 30, No. 3, Sept. 1958, pp. 359-376;

Part 4—The Air-Void System in Job Concrete,

J. Am. Concrete Inst., Vol. 30, No. 4., Oct. 1958, pp. 507-517.

[21] Mielenz, et al, op. cit., Part 1. [22] , Part 1, p. 113.

[23] , Part 3. [24] Mielenz, R. C, "Use of Surface-Active Agents in Concrete," Fifth International Symposium on Chemistry of Cement, Tokyo, 1968, Principal Paper, Part IV, Ses.sion 1, p. 13.

[25] Mielenz, op. cit., p. 24.

26] , p. 32.

[27] Mielenz, et al., op. cit., Part 1, p. 109.

39

Section 12. Water-Loss and Absorption of Concrete

R. L. Blaine and H. T. Arni

The relationships between portland cement characteristics and the loss of weight on

drying in air for 56 days and the absorption with subsequent 28 days storage in water of concretes were studied by computing multivariable regression equations with the aid of a digital

computer. The percentage absorption on rewetting was significantly related to the weight loss of concretes when air dried. The composition of the cement and the air-content of the concretes were also found to be related to the weight-loss and absorption as well as to ratios of weightgain/weight-loss. The effects of trace elements in the cements were generally of doubtful

significance in the drying and absorption tests.

Key words: Absorption; cement composition; concrete; loss on drying; portland cement;

trace elements.

Contents

Page

1. Introduction 41

2. Materials 42

2.1. Cements 42

2.2. Aggregates 42

2.3. Concrete 42

3. Tests and nomenclature 42

4. Statistical studies 42

5. Results of tests 43

5.1. Loss of Weight as a result of drying 43

5.1.1. Weight-loss of Series 0 concretes 43

5.1.2. Weight-loss of Series A concretes 48

5.2. Gain of weight as a result of immersion of air-dried specimens in water 51

5.2.1. Weight-gain of Series 0 concretes 51

5.2.2. Weight-gain of Series A concretes 51

5.3. Ratio of weight-gain to weight-loss 54

5.3.1. Weight-gain /weight-loss ratio of Series 0 concretes 54

Page

5.3.2. Weight-gain /weight-loss ratio for Series A concretes 56

5.4. Ratio of weight-gain minus weight-loss to weight-loss 59

5.4.1. Absorption ratio for Series 0

concretes 59

5.4.2. Absorption ratio for Series A

concretes 60

6. Discussion 65

6.1. Variables associated with weight-loss, absorption, and their ratios 65

6.2. Weight-loss and absorption versus dynamic

modulus 67

6.3. Air-content versus absorption and weight-loss 67

7. Summary and conclusions 67

8. References 68

1. Introduction

The resistance of concrete to attack by salts and other chemical reagents is dependent to some

extent on the quality of the concrete. Thus, a

concrete made with a high water/cement ratio is more subject to attack than one made of the same

cement with a low water/cement ratio. Also, a

concrete made with an adequate cement content

is more resistant than a leaner concrete. The de- gree of hydration at the time of exposure to destructive reagents can also be a factor. The

porosity and permeability of concrete may be

associated with all of these variables.

The amount of an aggressive solution which can

be absorbed is dependent to some extent on the

amount of water that is removed on drying.

Lea and Desch [1]^ have indicated that the

weight loss as a result of drying and the weight

gain with subsequent rewetting are dependent on

conditions of testing, such as temperature and

time of drying and rewetting. In this study the

specimens were dried under standard laboratoi-y

conditions, and the effects of different temperatures, humidities, and drying times were not

investigated.

' Figures in brackets refer to literature references at the end of this section (p. 68).

41
2. Materials

2.1. Cements

The Portland cements used in this study have

previously been described [2,3,4]- They consisted

of 199 commercially manufactured cements of different types, and were obtained from different areas of the USA, plus a few from other countries.

These cements were classified primarily on the

basis of their chemical analyses and physical

tests. 2 The chemical analyses and other tests indicated a fairly broad range of properties.

2.2. Aggregates

The aggregates were, as indicated previously,

[2] a high quality rounded quartzite coarse aggregate (White Marsh) and a sand from the same

source. The fineness modulus for the sand was

2.82, for the coarse aggregate, 6.82, and for the

combined aggregates 4.82.

2.3. Concrete

The procedures used in mixing and preparing

the 6- X 8- X 16-in concrete specimens have pre- viously been described in part 1, section 1 [2] as

well as in part 4, section 10 [5]. Two series of concretes both with a nominal cement content of

bags per cubic yard, were prepared. In one

series a constant water/cement ratio (w/c) of 0.635 was used. These concretes are referred to as the Series 0 concretes. In the other series the w/c

was adjusted, if necessary, to obtain a 5 + 1-in slump. These concretes are referred to as Series

A concretes.

3. Tests and Nomenclature

The 6- X 8- X 16-in (approximately 15- X 20-

X 40-cm) concrete specimens used for drying and

absorption tests were the same as those used for the volume change measurements reported in part 4 section 10 [5]. After casting, the specimens

were: (1) cured under wet burlap for the first 20

to 24 hours, (2) stored in the fog room at 100-

percent relative humidity until they were 14 days

old, (3) placed in laboratory air at 73 + 1 °F, and

50 + 5-percent relative humidity for 56 days, and

(4) immersed in water at 73 °F for an additional

28 days. Measurements were made of the weights

of the specimens at 24 hours, at 14 days, after

air-drying for 28 and 56 days, and after storage

in water for 28 days. Companion 3- X 4- X 16-in

beams made from the same concretes were given

the same treatment.

The percentage weight-loss of the specimens as a result of drying in laboratory air was calculated

from the ratio of the weight after the period of

air drying to the weight after removal from the

fog room at 14 days. This percentage is referred to as ODRY and ADRY for the Series 0 and A

concretes, respectively. The percentage gain of

weight when the air-dried specimens were placed

in water was calculated from the ratio of the

weight after water storage to the weight after air storage. This percentage is referred to as OWET

and AWET for the Series 0 and A concretes

respectivelv.

Various other notations are used for the various

ratios and differences of the percentage weight-loss

and percentage absorption. These are as follows:

ORWT and ARWT are used to designate the

ratios of OWET/ODRY and AWET/ADRY.

OWTR and AWTR are used to designate the

ratios (ODRY-OWET)/ODRY and (ADRYAWET)/ADRY respectively.

The air contents of the concretes are sometimes

referred to as such and at times by OAIR and

AAIR for the two series. The values were based on the percentage air by volume determined

gravimetrically according to ASTM Designation

C 138, on the plastic concrete, as indicated in part 1 section 1 [2]. Other abbreviations and symbols are the same

as those used in previous parts and sections of this

series of articles.''

4. Statistical Studies

The statistical techniques used to determine

and evaluate the independent variables associated

with the percentage-loss of weight on drying, or percentage weight-gain with subsequent storage

in water, or the various ratios and differences were the same as those described and used in pre- vious parts and sections of this series of articles. Multivariable regression equations were calcu2 Included were 82 Type I, 68 Type II, 20 Type III, 3 Type IV, and 12 Type V cements. Also included were 8 Type lA, 3 Type IIA, and 3 Type

IIIA cements.

lated by the method of least-squares to evaluate

the significance of the various independent variables associated with the dependent variables.

Residuals of multivariable equations were fitted by a least-squares method to other independent

variables and the reduction in variance calculated.

^ Among the abbreviations or symbols used are CsA, C3S, C2S, and C4AF

for the calculated potential compounds, tricalcium aluminate, tricalcium

silicate, dicalcium silicate, and tetracalcium aluminoferrite, respectively. Also, used are AE + NAE for air-entraining plus non-air-entraining cements, NAE for non-air-entraining cements, APF for air permeability

fineness, WAGN for Wagner turbidimeter fineness. Loss for loss on ig- nition, and Insol for insoluble residue.

42
If any of the additional independent variables

indicated a significant reduction in variance, they were tried in the equation and retained if the

coef./s.d. ratio was greater than 1.0.'' As in previous sections, comparisons were made

of the degree of fit of equations using commonly

determined variables as independent variables

and these together with minor and trace elements.

The level of significance of any reduction in the

S.D. values resulting from the use in the equation

of the additional independent variables was cal- culated for various pairs of equations or for an

equation and the S.D. values of the property of the concrete (as presented in footnotes in the

tables). The reduction in variance for the different

pairs of equations and critical "F" values which

must be equalled or exceeded for significance at the 5.0- and 1.0-percent significance levels are presented in a table summarizing these calculations. Equations were calculated using both the cal- culated potential compounds as well as the major

oxides, each together with other independent

variables. Equations were calculated for both the

AE + NAE cements and the NAE cements for

all the dependent variables.

Equations were also computed for the "odds"

and "evens" in the array of cements. If the coeffi- cients and coef./s.d. ratios of these equations were

in close agreement with those for the equation

computed for all cements, confidence in the rela- tionship was enhanced.

Although the drying and absorption tests were made on concretes made with each of the cements,

the calculations of the equations presented in this

section were limited to those for which trace elements had been determined. The concretes made with the three white cements and the one having a high autoclave expansion were excluded,

as were a few others that had large deviations

from the calculated relationship for no apparent

reason. The frequency distributions of the various

properties as well as calculated contributions to the various independent variables included all the

concretes for which values were available.

Equations presented in this article were selected

from a large number of trial equations indicating

the relationship of various independent variables

to percentage weight loss or gain, or the differences

and ratios. The differences and trends indicated

by these series of equations will be treated in subsection 6. Some of the limitations on interpretations of multivariable regression equations, as

well as the other statistical techniques used, have

been discussed in part 1 section 1, subsections 4.2,

4.3, and 5 [2] as well as in most of the preceding

sections of this series of articles.

Table 12-1. Frequency distribution of cements with respect to ODRY, the percentage weight loss of Series 0 concretes when air- dried for 56 days

Type cement

Percentage weight loss

1.8 to

2.0

2.0 to

2.2

2.2 to

2.4

2.4 to

2.6

2.6 to

2.8

2.8

to

3.0

3.0 to

3.2

3.2 to

3.4

3.4 to

3.6

3.6 to

3.8

3.8

to

4.0

4.0 to

4.2

4.2 to

4.4 Total

Number of cements

I 1 8 16 19 23

215

12

7

3

8

6

3

8

2 82

868

320

315

lA

II 2 10 17

13

1 5

1 2 IIA

III 4 6 53

1 IIIA

IV, V 1 1 3 3 4 1 1

Total 5 16 35 41 44 21 20 3 10 2 1 0 1 199

5. Results of Tests

5.1. Loss of Weight as a Result of Drying

3.1.1. Weight-Loss of Series O Concretes

The frequency distribution of percentage weightloss during drying of the Series 0 concretes is presented in table 12-1. The values ranged from

less than 2.0 percent to more than 4.2 percent and

* statistical terms and notations employed in this section are the same

as those in previous sections. For example, S.D. refers to the estimated

standard deviation calculated from the residuals of a fitted equation, or the estimated standard deviation about the average. Also, s.d. refers to the

estimated standard deviation of a coefficient of an independent variable used in a fitted equation, coef./s.d. the ratio of the magnitude of an esti- mated coefficient (of an independent variable used in an equation) to its estimated standard deviation, and "F" equals Fisher's ratio of variances.

there was an overlapping of the values for the

different types of cement.

Equations relating the variables associated with

the loss of weight of Series 0 concretes made with

AE -f NAE cements are presented in table 12-2.

As indicated in eq 1, an increase in C3S was asso- ciated with a decrease of the weight-loss and an

increase in C4AF with an increase of the weightloss. The reduction in variance was highly

significant."

» The reduction in variance or "F" ratios of comparable S.D. values are presented in table 12-33 together with the critical "F" ratios which must

be equaled or exceeded for significance at the oc = 0.01 and oc = 0.05 probability levels. Eq 0 as used in table 12-33 refers to the S.D. value of the corresponding dependent variable as given in footnotes in the tables

of equations.

43
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Other commonly determined variables, Na20,

K2O, SO3, Loss, and air content of the concrete,

also had coef./s.d. ratios greater than 1.0 (eq 2)

and, resulted in a further highly significant re- duction of variance. (See table 12-33, p 63).

The additional use of the trace elements Ba,

Cu, Rb, and Zr in eq 3 resulted in a slightly lower

S.D. value, but the reduction in variance was not

significant at the a = 0.05 level. (See table 12-33.)

The coefficients for the four trace elements as

well as loss on ignition were not highly significant,

and when equations 3A and 3B were calculated

for the "odds" and "evens" in the array of ce- ments, the coef./s.d. ratio was less than 1.0 for

each of these variables.^

Equation 4 was calculated using the major

oxides instead of the potential compounds as in eq 1. There was a highly significant reduction in the S.D. value, and with the use of other com- monly determined variables in eq 5 a further

significant reduction in variance was attained.

(See table 12-33) The additional use of the trace elements Ba, Cu, and Rb in eq 6 resulted in a

slightly lower S.D. value with a reduction of

variance significant at the a = 0.05 level. In eqs 6A and 6B calculated for the "odds" and

"evens," SO3, Loss, and the trace elements had

coef./s.d. ratios of less than 1.0 in one or the other

of the smaller groups of cements.

A similar series of equations calculated for the

Series 0 concretes made with the NAE cements

is presented in table 12-3. The use of the variables

C3S and C4AF in eq 1, or these together with

Na20, KoO, SO3, Loss, and air content in eq 2, each resulted in a highly significant reduction in variance. (See table 12-33.) The additional use of the trace elements Ba, Rb, and Zr in eq 3 did not

result in a significant reduction of variance.

' If a number of cements having higher than normal values for an inde- pendent variable are included in one of the two groups (the "odds" or "evens") by the arbitrary division of the cements, this distribution may

result in spurious coefficients for the variable. The estimated standard

deviations of the coefficients for the smaller groups were usually larger than when a combination of the "odds" and "evens" in the array of cements was used in calculating the equation. If the coefficients of both "odds" and "evens" of an independent variable are significant, a greater confidence can be placed in the equation, and in the association of that independent variable with the dependent variable. If the coefficient for a variable in either the "odds" or "evens" is not greater than its s.d., some

consideration may still be given to the larger groups of cements as indi- cating a possible relationship.

In eqs 3A and 3B calculated for the "odds" and

"evens" in the array of cements, the coef./s.d.

ratios for Loss, Rb, and Zr were less than 1.0 in one or both of the smaller groups.

The coef./s.d. ratio for CaO was less than 1.0

in eq 4 which was calculated using the major

oxides. The coefficient for this variable was, however, highly significant in eqs 5 and 6 where other

variables were also included. The use of the variables in eq 4 or these together with the additional

variables in eq 5 resulted in a highly significant

reduction in variance. (See table 12-33.)

The use of the trace elements Ba, Cu, Rb, and

Zr in eq 6 did not result in a reduction of the S.D.

value significant at the a = 0.05 level. Also, the

coef./s.d. ratios of the trace elements were less than 1.0 in one or both of the equations 6A and

6B calculated for the "odds" and "evens" in the

array of cements. The loss on ignition of the

cements also had a coef./s.d. ratio less than 1.0 with the smaller groups.

The calculated contributions of the independent

variables to the percentage weight loss resulting

from drying are presented in table 12-4 together

Table 12-4. Calculated contributions of independent variables

io ODRY, the percentage loss of weight resulting from air- drying of Series O concretes made of AE + NAE cements

Calculated range of Independent Ranges of Coefficients Calculated contribuvariables variables from eq 3 contributions tions to (percent) table 12-2 to ODRY ODRY

Const. = -1-4.24 C3S 20 to 65 -0.02268 -0.45 to -1.47 1.02 CiAF 1 to 16 -1-0.03219 -1-0.03 to -1-0.51 0.48 NajO 0 to 0.7 -0.5326 0 to -0.37 0.37 K2O 0 to 1.1 -0.594 0 to -0.65 0.65 SOa... 1.2 to 3.0 -0.249 -0.30 to -0.75 0.45 Loss* .

.

0.3 to 3.3 -0.0654 -0.02 to -0.22 0.20 Air-content. _ 0 to 11 -1-0.0647 0 to -1-0.71 0.71 Ba* 0 to 0.2 -1-1.012 0 to -1-0.20 0.20 Cu* 0 to 0.05 -1-2.702 0 to -1-0.14 0.14 Rb* 0 to 0.01 -16.13 0 to -0.16 0.16 Zr* 0 to 0.5 -0.573 0 to -0.29 0.29

*Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. with the calculated ranges of these contributions.

These contributions and ranges were calculated

from the coefficients of the independent variables

in an equation and the approximate ranges of

these variables in the cements of this investigation. These calculated values are estimates based

Table 12-5. Frequency distribution of cements with respect to ADRY, the percentage weight loss of Series A concretes when air- dried for 56 days

Percentage weight loss

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 Type cement to to to to to to to to to to to to to Total

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

Number of cements

I 2 6 62

8

1

7

22

5 21

19

1 11

1

1

12 5 5 2 79

8

67

320

3

15

lA

II 1 9

1 8 3 6 IIA

III 2

1 32

6 1 IIIA

IV, v... 1 1 1 5 1 4 1 1 Total 6 11 25 55 34 27 16 12 3 6 0 0 1 195

46
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47
on a single equation, and somewhat different

values would be obtained by use of other equations. Similar computations for calculated contributions to dependent variables have also been

made from corresponding equations in order that

the trends may be followed more easily^

5.1.2. Weight-Loss of Series A Concretes

The frequency distribution of the weight loss during drying of the Series A concretes is pre- sented in table 12-5. There was an overlapping of

the values for the concretes made of the different

types of cement and a broad distribution of values.

Equations relating the variables associated with

the loss of weight of Series A concretes made with

AE + NAE cements are presented in table 12-6. In eq 1 the coef./s.d. ratio for C3A was less than

1.0 but in eq 2, where other commonly determined

variables were included, the coefficient was highly

significant. With water/cement ratio and air content included with the independent variables in

eq 3, the coef./s.d. ratio for C3A was lowered.

The relationship of C3A, SO3, and K2O to water

requirements of Series A concretes was previously

reported in eq 5, table 2-20 [2]. The use of C3A, C3S, and C4AF as independent

variables in eq 1; these plus Na20, K2O, SO3, and

Loss in eq 2; and the further addition of w/c and

air content in eq 3 resulted for each of the equations in a highly significant reduction in variance.

(See table 12-33.) The additional use of the trace elements Ba, Cu, Rb, and Zr as independent variables in eq 4 resulted in a slightly lower S.D. value,

and the reduction in variance was significant at the a = 0.05 level. Using the major oxides in eq 5 instead of the

calculated potential compounds also resulted in a

highly significant reduction in variance. The additional use of w/c and air content as independent

variables in eq 6 resulted in a further reduction in the S.D. value. However, addition of the trace

elements Cu, Rb, and Zr in eq 7 did not result in a significant reduction in variance. (See table

12-33.)

A similar series of equations for the Series A

concretes made of NAE cements is presented in table 12-7. The coefficients and coef./s.d. ratios

of the independent variables are in reasonable

agreement with those of table 12-6 where the AE

cements were included. One exception may be

noted; the coef./s.d. ratio for the air content was

lower when only the NAE cements were included

as in table 12-7. The use of trace elements together

with commonly determined variables did not

result in a significant reduction in variance. (See

table 12-33.)

Using the coefficients of the independent variables of eq 4, table 12-6, and their ranges of values,

computations were made of the calculated contributions to the ADRY values as well as the

calculated ranges of these contributions. These

calculated values are presented in table 12-8.

Table 12-8. Calculated contributions of independent variables

to ADRY, the percentage loss of weight resulting from air- drying of Series A concretes made of AE + NAE cement

Independent

variables Range of variables

(percent)

Coefficients from eq 4 table 12-6Calculated

contributions

to ADRY

Calculated range of contributions to ADRY

Const. = -0.97 C3A 1 to 15 +0.0232 +0.02 to +0.34 0.32 CsS... 20 to 65 -0.0221 -0.44 to -1.43 0.99 C4AF 1 to 16 +0.0524 +0.05 to -1-0.83 0.78 Na20 0 to 0.7 -0.5794 0 to -0.40 0.40 K2O 0 to 1.1 -0.6528 0 to -0.78 0.78 SO3 1.2 to 3.0 -0.2455 -0.29 to -0.74 0.45 Loss 0.3 to 3.3 -0.0898 -0.03 to -0.30 0.27 w/c 0.55 to 0.72 +7.654 +4.21 to +5.51 1.30 Air-content_

.

0 to 13 +0.0594 0 to +0.77 0.77 Ba* 0 to 0.2 +1.119 0 to +0.22 0.22 Cu* 0 to 0.05 +3.92 0 to +0.20 0.20 Rb* ___ 0 to 0.01 -14.56 0 to -0.15 0.15 Zr* 0 to 0.5 -0.62 0 to -0.31 0.31

' Corresponding tables for equations calculated for AE + NAE cements,

using the calculated potential compounds, other commonly determined

variables, and trace elements having a coef./s.d. ratio greater than 1.0

will be presented for other dependent variables. Summary tables (tables 12-34 and 12-35) are also presented for greater ease in comparing similar equations for the NAE cements.

*Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. Increases in C3A, C4AF, w/c, and air content were

associated with increases in values for weight-loss. Increases in C3S, Na20, K2O, SO3, and loss were

associated with decreases in the values for weightloss. Variations of w/c, C3S, C4AF, K2O, and air content had the highest values for the calculated

range of contributions to the values for weight-loss.

Table 12-9. Frequency distribution of cements with respect to OWET, the percentage weight gain of Series O concretes when air- dried specimens were placed in water for 28 days

Percentage weight gain

Type cement

1.8 to

2.0

2.0 to

2.2

2.2 to

2.4

2.4 to

2.6

2.6 to

2.8

2.8

to

3.0

3.0

to

3.2

3.2

to 3.4

3.4 to

3.6

3.6 to

3.8

3.8 to

4.0 Total

Number of cements

I 2 13 24 26 9 4 4 82 lA 1 2 5 8

II 1 7 11 19 12 6 6 4 1 1 68 IIA 1 1 1 3 III 3 7 4 3 3 20 IIIA 2 1 3 IV, V 1 1 3 3 1 3 1 1 1 15 Total 6 27 40 51 28 17 16 7 3 2 1 199

48
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50
5.2. Gain of Weight as a Result of Immersion

of Air-Dried Specimens in Water

5.2.1. Weight-Gain of Series O Concretes The frequency distribution of the cements with

respect to the weight gain of Series 0 concretes,

moist cured for 14 days then air dried for 56 days,

and then placed in water for 28 days, is presented

in table 12-9. There was a broad distribution of values and an overlapping of values obtained with

concretes made of the different types of cement.

Equations relating the variables associated with

the percentage gain of weight on resoaking for the

Series 0 concretes made of AE + NAE cements

are presented in table 12-10. Equation 1 indicates a significant relationship between weight-gain and

weight-loss during the period of drying in air. The

S.D. value obtained for eq 1 was much smaller

than was obtained in other equations where air content and other independent variables were

used. As indicated in eq 2, an increase in the air content was associated with an increase in the

gain of weight of the concrete when rewetted. The

additional use of C3S and C4AF in eq 3 caused a

significant reduction in the S.D. value, and in eq

4, where the variables Na20, K2O, SO3, and Loss

were included, a further significant reduction was

obtained. (See table 12-33.) The trace elements

Cu, Rb, Zr, and Ba all had coef./s.d. ratios greater

than 1.0 in eq 5 where all cements were included,

but the coef./s.d. ratios for Rb, Zr, and Ba were

less than 1.0 in eqs 5A or 5B, the "odds" or "evens" in the array of cements.

Equations 6, 7, and 8 were calculated using the

major oxides instead of the calculated potential

compounds as in eqs 3, 4, and 5. There was a significant reduction in variance in the successive

eqs 6, 7, and 8 (See table 12-33.), but the S.D.

values were about twice as large as that for eq 1 where the weight loss was used as an independent

variable. The coef./s.d. ratio of CaO was less than

1.0 in eq 6 but highly significant in eqs 7 and 8. Equations calculated to indicate the independent variables associated with the weight-gain of Series 0 concretes made with NAE cements are presented in table 12-11. The independent variables, their coefficients, and the coef./s.d. ratios were in reasonable agreement with those presented

in table 12-10 where the AE cements were in- cluded. It may be noted that SO3 had a coef./s.d.

ratio less than one in eqs 4A and 7A calculated

for one of the smaller groups of cements.

Using the coefficients of the independent variables of eq 5, table 12-10, and their ranges of values, computations were made of the calculated

contributions to the OWET values, as well as the

calculated ranges of such contributions. The calcualted values are presented in table 12-12. Increases Table 12-12. Calculated contributions of independent vari- ables to OWET, the percentage gain of weight with resoaking

of air-dried Series O concretes made of AE + NAE cements

Independent

variables Ranges of variables

(percent)

Coefficients from eq 5 table 12-10

Calculated

contributions

to OWET

Calculated

range of contributions to OWET

Const. = +3.84

Air-content_ _ 0 to 11 +0.09755 0 to +1.07 1.07 CsS 20 to 65 -0.01967 -0.39 to -1.28 0.89 CiAF 1 to 16 -fO. 02997 +0.03 to +0.48 0.45 NazO 0 to 0.7 -0.6705 0 to -0.47 0.47 KjO 0 to 1.1 -0.5972 0 to -0.65 0.65 SO3 1.2 to 3.0 -&.183 -0.22 to -0.55 0.33 Loss*. - 0.3 to 3.3 -0.0669 -0.02 to -0.22 0.20 Cu 0 to 0.05 +4.89 0 to +0.24 0.24 Rb* 0 to 0.01 -18.5 0 to -0.18 0.18 Zr* 0 to 0.5 -0.8074 0 to -0.41 0.41 Ba* 0 to 0.2 +0.891 0 to -0.18 0.18

*Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. in the air content of the concretes, C4AF, and

possibly Cu were associated with increases in the

values for weight-gain. Increases in C3S, Na20,

K2O, and SO3 were associated with decreases in the values for weight-gain.

5.2.2. Weight-Gain of Series A Concretes The frequency distribution of the percentage

gain of weight when resoaking air-dried concretes made of AE + NAE cements is presented in table

12-13. There was a broad distribution of values

and an overlapping of the values of the different

types of cement.

Equations relating the variables associated with

the weight-gain of the Series A concretes made

with AE + NAE cements are presented in table

12-14. No significant relationship was found in

Table 12-13. Frequency distribution of cements with respect to AWET, the percentage weight gain of Series A concretes when air- dried specimens were placed in water for 28 days

Percentage weight gain

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 Type cement to to to to to to to to to to to Total

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Number of cements

I 2 8 16

216

14

1

1

27

415

13

2

13

14

6 2 4 1 79

867

3 20

3

15

lA

11 1 4 7

1

1

3 3 3 2 IIA m 3

1 4 4 mA 1 IV, V 5 4 3 1 1 Total 7 16 41 51 38 19 5 10 5 2 1 195

51
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52
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AWET

s.d.

AWET

s.d.

AWET

s.d.

AWET

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AWET

s.d.

AWET

s.d.

AWET

s.d.

AWET

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AWET

s.d.

AWET

s.d.

AWET

s.d.

AWET

s.d.

Note rH »H

N CO rH

N

dd

Nm 'J' 4A. 4B_ <!

t>

m 00

223 S a a as 0) OJ D s a Es y y o «

CO CM rH , CO 00 X-rt

rH

X

__ ^ CD r-TcM CO^

+J +J

O

OO OrX

53
eq 1 where the water/cement ratio was used as an independent variable. (See table 12-33.) The

use of the potential compounds C3A, C3S, and

C4AF in eq 2 resulted in a significant lowering of the S.D. value. The sign of the coefficient for C3A

was negative and not highly significant in eq 2, but in eq 3 where Na20, K2O, SO3, and Loss were

included as variables, the sign was positive, and

the coefficient was highly significant. Including

the trace elements Cu, Mn, Ba, Co, and Zr with

the other independent variables in eq 4 resulted

in a significant reduction in variance. (See table

12-33.) With the use of water/cement ratio in addition to all of these independent variables as

in eq 5, the reduction in variance due to the one added variable was significant at the a = 0.05

level. A corresponding series of equations, (eqs 6, 7, and 8) calculated with the major oxides, resulted

in S.D. values and "F" ratios comparable to those

obtained in eqs 3, 4, and 5 where the potential

compounds were used. The coef./s.d. ratio for Mn

was less than 1.0 when used with these variables,

and therefore was not included in eqs 6, 7, and 8. In equations 4A, 4B, 7A, and 7B calculated for the "odds" and "evens" in the array of cements.

Loss, Fe203, Mn, Ba, Co, and Zr had coef./s.d.

ratios less than 1.0 in one or both of the pairs of equations calculated for the smaller groups of cements.

A similar series of equations indicating the independent variables associated with the absorption

of Series A concretes made of NAE cements is presented in table 12-15. The coefficients, the

coef./s.d. values and the S.D. values of the equations are in reasonable agreement with those pre- sented in the previous table where the AE cements

were included. The coefficients for water/cement

ratio were somewhat greater in table 12-15, eqs 5 and 8, than they were in corresponding equations

in table 12-14.

Using the coefficients of the independent variables of eq 4, table 12-14, and their ranges of values, computations were made of the calculated

contributions to the AWET values, as well as the

calculated ranges of such contributions. The calculated values are presented in table 12-16. Increases

Table 12-16. Calculated contributions of independent vari- ables to AWET, the percentage gain of weight with resoaking

of air-dried Series A concretes made of AE + NAE cement

Lialculated Independent xCange 01 ooerncients Calculated range of variables variables from GQ 4 contributions contribu-

(percent) to A W Hj 1 tions to AW Sit I

*^onsc. — -TO. oy C3A _ 1 to 15 1 n AQ1 A Q -ru.uo to -ru.4 ( 0.44 on t-n fit; to 00 —V.U104D — yj.o 1 to — i.^u 0 83

1 to 16 j_n n^i 7/1 ~j~\j.\Joi 1 ft 0 48 NasO 0 to 0.7 -0.73 0 to -0.51 o'.51 0 to 1.1 -0.7508 0 to -0.83 0.83

SO.1* 1.2 to 3.0 -0.1112 -0.13 to -0.33 0.20 Loss* _ _ _ 0.3 to 3.3 -0.0643 -0.02 to -0.21 0.19 Cu 0 to 0.05 +6.21 0 to +0.31 0.31 Mn* 0 to 1.0 +0.2703 0 to +0.27 0.27 Ba* 0 to 0.2 +0.8975 0 to +0.18 0.18 Co* 0 to 0.01 +23.4 0 to +0.23 0.23 Zr* 0 to 0.5 -0.6765 0 to -0.34 0.34

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. in C3A, C4AF, and possibly Cu were associated

with increases in absorption. Increases in C3S,

Na20, and K2O were associated with decreases in absorption. Indications of the effects of SO3, Loss,

Mn, Ba, Co, and Zr were of doubtful significance.

Variations in C3S and K2O had the highest values

for the calculated range of contribution to gain of weight when the air-dried concrete specimens were

placed in water.

5.3. Ratio of Weight-Gain to Weight-Loss

5.3.1. Weight-Gain/ Weight-Loss Ratio of Series O

Concretes The frequency distribution of the weight-gain/

weight-loss ratio of the Series 0 concretes is pre- sented in table 12-17. There was a broad distri- bution of values and an overlapping of the values

obtained for the different types of cement. About

70 percent of the concrete specimens absorbed less water in 28 days of soaking than they had lost in 56 days of drying. The other specimens including

most of those made of the air-entraining cements

had a gain /loss ratio greater than one. Equations relating the variables associated with

the gain/loss ratio for the Series 0 concretes made

of AE + NAE cements are presented in table

12-18. Equation 1 indicates that the gain/loss

ratios are significantly related to the air contents

of the concretes. With the additional use of comTable 12-17. Frequency distribution of cements with respect to ORWT, the ratio of percentage weight gain divided by the per- centage weight loss of Series O concretes. ORWT = OWET/ODRY

Type cement

Absorption ratio

0.82 to

0.85

• 0.85

to

0.88

0.88

to

0.91

0.91

to 0.94

0.94

to

0.97

0.97

to

1.00

1.00 to

1.03

1.03 to

1.06

1.06

to

1.09

1.09 to

1.12

1.12 to 1.151.15

to

1.18

1.18

to

1.21 Total

Number of cements

I 2 10 28 21 6

17

12

3

9

14

2

2

1

2

1

1 82

868

320

315

lA 2 II 3 2 18 24 4 IIA

III 1 1 4 3 2

1 3 1 IIIA 1 1 rv, V 3 8 1 3 Total 1 5 12 50 57 18 32 9 8 3 3 0 1 199

54
ONla TP

cm o o doI ^

(Deo o o oo

0(0 o t00 CO o o O lO

1-100 O rj«

t> 00

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do* do* o c> d d

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O o o o o o o o o d d

Tf ttO -'t TP N OOo q dd+^

to t> oo

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to

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ORWT

s.d.

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ORWT

s.d.

ORWT

s.d.

ORWT

s.d.

ORWT

s.d.

ORWT

s.d.

ORWT

s.d.

ORWT

s.d.

Co

cog:

ca ^

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tow

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TP CM o o qqdd+^

U5

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CJ to ^ o O o

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CM toO o o o o o o q q dd

to CM o o o o dd

ooddI ^ o o o o o to

CO o ooo o o o q q dd

tr- Oi O

to CO o o q q dd

00 to

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CM

qq ddI ^

co ^

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©

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q

W o o q ^ © q ^ © oq ^ © q o © © ^ O q q

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q

q

q

q dd © d d d d d d d d d dd d d d d +^ +^ +^ +^ 4-^

CO 00

CO o

Oi o

TfCO

in CO

00 o

ai04

Tf CO

00 o

c- in inTf

00 o

OO-H Tf CO

Tf in in CO

00O 00 o

Tf CO

00 o

00 in

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m o o

Bj-d O M o o

Eh

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+-'

II II O n o o

EhO in

or o HZ

55
monly determined variables in eq 2 a further

highly significant reduction of variance was

achieved. (See also table 12-33.) The use of Cu

and Mn as independent variables together with

the other independent variables in eq 3 resulted

in a slightly lower S.D. value, but, as indicated in table 12-33 this was significant at the a = 0.05

level. Equations 3A and 3B, calculated for the "odds"

and "evens" in the array of cements, indicated

that C3A, Loss, Cu, and Mn had coef./s.d. ratios

less than 1.0 in one or the other of the equations

for the smaller groups of cements.

In eqs 4 and 5, the oxides were used as independent variables instead of the potential compounds. A highly significant reduction of variance

resulted from use of the commonly determined

variables in eq 4, but with the additional use of the trace elements in eq 5 the reduction of vari- ance was significant at the a = 0.05 probability

level. A corresponding series of equations for the

gain/loss ratio of Series 0 concretes is presented

in table 12-19. The coef./s.d. ratio for the air content in eq 1, table 12-19, was smaller than the

corresponding one .in table 12-18 where the AE

cements were included. The use of commonly

determined variables C3A, C4AF, Na20, MgO,

APF, and Loss in eq 2 resulted in a highly significant reduction in variance. The additional use of Cu and Mn in eq 3 resulted in a reduction of variance significant at the a = 0.05 level. (See

table 12-33.)

The use in eqs 4 and 5 of the oxides AI2O3 and

Fe203 instead of the calculated potential compounds resulted in an equivalent reduction of the

S.D. values.

Equations calculated for the "odds" and "evens"

in the array of cements (eqs 3A, 3B, 5A, and 5B)

had instances where the coef./s.d. ratio was less than 1.0 for C3A, AI2O3, Fe203, Loss, and Cu.

Using the coefficients of the independent variables of eq 3 of table 12-18 and their ranges, computations were made of the calculated contributions to the OWTR ratio, as well as the calculated

ranges of such contributions. The calculated values

Table 12-20. Calculated contributions of independent vari- ables to ORWT, the ratio of percentage absorption to percentage weight loss on drying of Series O concretes made of AE + NAE cements

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq 3

table 12-18

Calculated

contributions

to ORWT

Calculated range of contributions to ORWT

Const. = +0.839

Air-content-

_

0 to 11 +0.012 A 4-.. _1_A 1 QO U to -rU.io^ 0.132 CsA** 1 to 15 -0.0016 -0.002 to -0.024 0.022 C4AF" 1 to 16 -0.00301 -0.003 to -0.048 0.045 NazO 0 to 0.7 -0.0632 0 to -0.044 0.044 MgO 0 to 5.0 -1-0.00655 0 to +0.033 0.033 APF *2500 to 5500 +0.0000431 +0.107 to +0.237 0.130 Loss** 0.3 to 3.3 -0.0094 -0.003 to -0.031 0.028 Cu 0 to 0.05 +0.697 0 to +0.034 0.034 Mn** 0 to 1.0 -0.0450 0 to -0.045 0.045

*cmVg.

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. are presented in table 12-20. Increases of the air content, fineness, and possibly MgO and Cu were

associated with an increase of the ORWT ratio. Increase in Na20 was associated with a decrease

of the ORWT ratio.

5.3.2. Weight-Gain/Weight-Loss Ratio for Series A

Concretes The frequency distribution of the ratio of per- centage absorption to the percentage weight loss of Series A concretes is presented in table 12-21.

There was a broad distribution of values and an

overlapping of the values for the different types

of cement. About one-fourth of the specimens had

a slightly greater absorption than loss on drying,

and these included concretes made with 11 of the

14 air-entraining cements.

Equations indicating the variables associated

with ARWT are presented in table 12-22. The

use of the commonly determined variables, air content, Na20, MgO, and APF in eq 1 resulted in a significant reduction in variance. The additional use in eq 2 of C4AF, Ba, Cu, SrO, and V resulted

in a reduction of variance significant at the 5.0- percent level. (See table 12-33.) In equations 2A and 2B calculated for the

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

coef./s.d. ratios for C4AF, MgO, Ba, SrO, and V

Table 12-21. Frequency distribution of cements with respect to ARWT, the ratio of percentage weight gain divided by the per- centage weight loss of Series A concretes. ARWT = AWET/ADRY

Absorption ratio

0.82 0.85 0.88 0.91 0.94 0.97 1.00 1.03 1.06 1.09 1.12 Type cement to to to to to to to to to to to Total

0.85 0.88 0.91 0.94 0.97 1.00 1.03 1.06 1.09 1.12 1.15

Number of cements

I 3 12 20 23

3

17

8 7

210

13

1

2

2

3

12

3

12

14

1 79

867

320

315

lA

II 1 2 3 22 7 IIA

Ill 1 2 6 2 IIIA 2 IV, V 1 2 6 4 2 Total 1 5 17 46 55 21 24 12 11 1 2 195

56
6 Co s s

lie

&>

K ^ o

CO ^ oOI aa< < s

inCON

CON d d

U5

O

dd

eoeo o o

00 o d d00 ^ d d

N OO

OJ

O

INi-Id

IC

O (N 00 CO o o

(N CO o d OO

iH

O

CO o

Oi 00

lO CO o q d dI ^

com

eoN q q ddI ^ OlO

O

dddd

coco q q d dI ^

00 o d d

qq

dd

00 OJ d d

U5

O rH t> 1-1 CO OO

NCO d d

OO

N o o o o o OO

dd+^ o o o o OOO O d d

rHiA OC00 0> N rH O MO O O O O O O O OO OO

OO OO

i-HCD ^ o OOO OO q q d d +^CO OCD

c^i o o o o o o o oqdd4-""

Oi 5D

1-1

O

Oo o o o q q . dd

00

a i-t o o oo o o q q dd

Otr0^ o O OoO q q dd o o qqd d

OS CO iCO

irt CO o o q q d d

4-^

00 rjt O O q q d d

OON

OS iC o o o o

COt- o o q q d d

00 o>

CO C4 O O o o

00 COo lOeo o o q q dd

U5 CO CO CO

00o o qqdd+^

00

N o o o o

«0o o o o

CO --t in ^CO (O o to CO CO CO q q q q dd d d

r-l CO CO in

to i-f »H

O

tXN trW q q q q dd

CO

to CO o o ooI ^ oo

oco

coo OiM o o

t>

00 -'t o o o q d dI ^

00

w CJ 00

Tl* "£> o o q q d dI ^ M CO

00COM o o o o ooI ^

CO CO t> 1-1 o o o o

oco

coco

t>1-l o o o o

to CO CO o ino Ciy-f in C^J 1-1 CO O O 1-1 o o o o o

CO 00

CO CO

O CO

CO ^ f Tf o o o o oo o o

t> IN lO o o o o o o o o o o o o o oo o o

t>co

in Oi N o oo

t- in

t- CM 00 O

OCO

Ol o

t- CO CD

O ^ d ^

OlO 00 o

in

w

O CO

OS o

astr- oOl o i ?s o o

II II oo o o

4-^ o o oo o o

II II

coco

iOt>

in CO q q ddI ^

CO 00

<NO

O

O o o o o o o q q d d

CM tin ai

in (N o o q q d d

-«t 1-1 1-1 CO

CO

O CO 1-1 CO CO t- o o o o

CD 00

ino o o o

CO

O CO

ai "H CO CO

tH CO CD .-1 iH O O O OO O O o

t> CO

in Oi

CM o o o

CO CO 00 iH 00 o us o o o

ARWT

s.d.

ARWT

s.d.

ARWT

3.d.

ARWT

s.d.

ARWT

s.d.

ARWT

s.d.

ARWT

s.d.

ARWT

s.d.

ARWT

s.d.

ARWT

s.d.

Note IN CO CO iH

HZ i <

IN

n

(N CO

5A 5B

CO - CO ' . in > d o . : Q

„- : o c cn

a Its ass:

.|J 1U

C (V) « t. u 0) u W rH 00

(DO 0) 0) o oo o o o 2ZZ

57
2^

00

ood d

to as

00 CO o o d d

00 CO

lO o d d

t- CO

to eo

00 o t>eo

t> eo q q d dI ^

00 <^

eo 00 o eo q N dd

iO CO

00 U5 O O w d

M o

(N IN

eo to o 00

00 CO o o

\n o

CO-*

OS CO

r-t CO o o o o o o

tOiiS 00CON d d

U5CO

to

a 00 CO o o

OtO

to o dd o *

t- CO

to CO d d

Oi o

c- eo

c- to o o o to 00 tr- ddI —

»oeo

00 10 o o 00 00

to to SOOto

to Tf

OS CO

tH CO 00 o o

eooo

00 eoO o o 00o o dd4-"^

Oi c- U3tO

r^ o 00

00o o

.H rH i-H

O

OO

Oqqd d o o o o o o o o dd+^

la c- eoto

rH o o o o o o o o q d d

0000

t- to 1-10 00o o 00qod d 4-"^

ITS to rHO 00O O 00q q d d o o o o o o q q dd

00 00

OS OS

l-H

O o o o o o o q q d d

to

N OS CO CI 00

qqdd

OS-* o o in CO o o o q d d

1-1

M 00 o o o q dd o o 00 -H

CO Til o o q o dd+^ ^ 00

05 iO CJ O O o q dd+^

<*00 00s

CO(M 00o q d d

00 * 00ineo 00oqdd+^ o o q o dd

coco NONN

t-to 000

00 eo q q dd

ost- 000

1-H u3 ca * d i-< d o o

CO toO 00o o oqdd+^

t-os 000 t-o ^os COf ION 00 00 q q q q d d o o

•11

coctc o

tN qqdd1 ^

coco

10 ^

tON O O ddI

eo CO

10 to toco o q ddI

coos

OS 00

to

N o o

U5C0

la th C- C>1 o o

OS 00

eo

©N 00

00

eo CO into

to CO 00

ddI ^

eooo ii5eo OS 00

to

N tN 00 00 O O

N tr- io to

CO f o o 00 o oI -

C- OS 00 CO O 00 o o qqddI

^N^(O N toO oq

dd

eooo N N o o o o o o 00I ^ f N o o o q ddI "

00o o OS * 00

qqdd

OS OS

to ^

t-00o o

U5 0S

OS 10 00o o d d

0000 * N U5 to O O o o d d

U3 Tf o o q o d d

10

O

CO -ef 00O Ot- * O O o q d d

10 eo

10 OS

OS 10 O o o o

OS 00 * N ya to o o o q d d o o

<*

N 00 00

U3 •* o o o o o o o q d d

Ss o to es

&<

tu

CO

1-1 am< H2

t-io * OS N O O

t- * * OS N O o q ddI

t>to

00

N 00 O 00 00 +- +^

II II II II

eo OS

•-H *

OS

q dd

N *

OS o dd

O

N OS

OS

O NNoeo q o dd+^ 00

tos q o dd

II II II II II II <

i-H

*t- N * q o dd

II II o o

<; CD

°^ II c o c O <V 0) 0)

•fjn OS o ii u o o « rH-IO ^ eOOOOO -HNCO

OS

O OS 0) 0) or 000

58
were less than 1.0 in one or the other of the

smaller groups.

The use in eq 3 of ADRY, the percentage loss on drying as an independent variable, together

with those previously mentioned, resulted in a

further significant reduction of variance. In eqs

3A and 3B, calculated for the "odds" and "evens"

(not presented in the table), there were instances

where the same independent variables had coef./

s.d. ratios less than 1.0 as was indicated in eqs 2A

and 2B. Equations 4, 5, and 6 were calculated

using Fe203 instead of C4AF as an independent

variable. The coef./s.d. ratio for Fe-iO^ was less than 1.0 in eq 4 and of doubtful significance in eqs 5 and 6. The use of the trace elements in eq 5

resulted in a reduction of variance significant at

the 5.0-percent level. (See table 12-33.)

A corresponding series of equations for the NAE

cements is presented in table 12-23. The coeffi- cients, the s.d. values for the coefficients, and the

S.D. values are in reasonable agreement with those

of the previous table where the AE cements were

included.

Using the coefficients of the independent variables of eq 2 table 12-22 and the ranges of these

variables, calculations were made of the estimated

contributions to ARWT. The results of these

calculations are presented in table 12-24 together

with the calculated range of these contributions.

Table 12-24. Calculated contributions of independent variables to ARWT, the ratio of absorption to weight loss on

drying of Series A concretes made of AE + NAE cements

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq 2

table 12-22

Calculated

contributions

to ARWT

Calculated range of contributions to ARWT

Const. = +0.904

Air-content.. 0 to 13 +0.0073 0 to +0.095 0.095 C4AF**__. 1 to 16 -0.00276 -0.003 to -0.044 0.041 NajO 0 to 0.7 -0.0634 0 to -0.044 0.044 MgO**-,.. 0 to 5 +0.00559 0 to +0.028 0.028 APF *2500 to 5500 +0.0000195 +0.049 to +0.107 0.058 Ba** 0 to 0.2 +0.195 0 to +0.039 0.039 Cu 0 to 0.05 +0.985 0 to +0.049 0.049 SrO** 0 to 0.4 -0.0596 Oto -0.024 0.024 V** 0 to 0.1 -0.315 0 to -0.032 0.032

*cm2/g.

**Coeffieient of doubtful significance as coef./s.d. ratio was less than 2.0.

Increases of the air-content, fineness, and possibly

Cu were associated with an increase of the ARWT

ratio. Increase of Na20 was associated with de- crease of the ARWT ratio.

5.4. Ratio of Weight-Gain Minus Weight-Loss

to Weight-Loss

5.4.1. Absorption Ratio for Scries O Concretes The frequency distribution of the cements with

respect to OWTR, the ratio (ODRY-OWET)/

ODRY, is presented in table 12-25. There was a

fairly broad distribution of values and an over- lapping of the values obtained with the different

types of cement.

Equations are presented in table 12-26 indicating the independent variables associated with

OWTR. The use of the commonly determined in- dependent variables C3A, C3S, C4AF, NaaO, SO3,

APF, Loss, MgO, and air content in eq 1 resulted

in a significant reduction of variance. The additional use of Cu and SrO in eq 2 resulted in a

further reduction of variance significant at the

5.0-percent level. In eq 2B the coef./s.d. ratios of C4AF, NaaO,

and Cu were less than 1.0 for this group of results. Equations 3 and 4 were calculated using the

major oxides instead of the calculated potential

compounds. The coef./s.d. ratios for SO3, Loss,

and MgO were less than 1.0 when included with

these variables and were not retained in these

equations.

The corresponding series of equations for the

NAE cements is presented in table 12-27. The

coefficients, their s.d. values, and the S.D. values

of the equations are in reasonable agreement with

those of the previous table where the AE cements

were included.

Using the coefficients of the independent variables of eq 2, table 12-26, together with the ranges

of these variables, calculations were made of the

estimated contributions to OWTR and the ranges

of such contributions. These calculated values are presented in table 12-28. Increases of air content,

fineness, and possibly C3S, Cu, and MgO were

Table 12-25. Frequency distribution of cements with respect to OWTR, the ratio of the difference between weight loss and weightgain to the weight loss of Series O concretes. OWTR = (ODRY - OWET)/ODRY

Type cement

Absorption ratio

-0.21

to -0.18

-0.18

to -0.15

-0.15

to -0.12

-0.12

to -0.09

-0.09

to -0.06

-0.06

to -0.03

-0.03

to0

0

to +0.03

+0.03

to 0.06

0.06

to

0.09

0.09

to

0.12

0.12

to 0.15

0.15

to

0.18 Total

Number of cements

I 2

1

12

1

13

4

2

2

0

1

1

14

1 15

21

1 25

29 10 3 82

868

320

315

U

II 18 2 3 lU...

Ill 4 2

1 5 5 1 1 Ilia 1 1 IV, v 1 3 7 4

Total 1 0 1 4 7 11 7 38 59 52 12 6 1 199

59
Table 12-26. Coefficients for equations for AE + NAE cements relating the ratio of gain with water storage divided by the percentage weight-loss of Series 0 con

Eq. No.

1 __.

2

2A

2B

3

4

4A

4B

Note

1

1

2

2

1

1

2

2

OWTR

s.d. OWTR

s.d. OWTR (odd)

s.d. OWTR (even)

s.d. OWTR

s.d. OWTR

s.d. OWTR (odd)

s.d. OWTR (even)

s.d.

Const.

: +0.181

(0.035) +0.193

^ (0.035) +0.184

(0.049) +0.221

= (0.060)

: -0.168

= (0.138)

: -0.217

- (0.138)

^ -0.234

= (0.189)

= -0.231

= (0.208)

CaA

+0.00299

(0.00114) +0.00199

(0.00122) +0.00300

(0.00182) +0.00183

(0.00172)

C4AP

-0.00087 +0.00220

(0.00046) (0.00146) -0.00094 +0.00257

(0.00045) (0.00147) -0.00061 +0.00476

(0.00058) (0.00215) -0.00164 * +0.00140

(0.00074) (0.00217)

SiOt AI2O3

+0.0095 +0.0162

(0.0044) (0.0056) +0.0113 +0.0155

(0.0044) (0.0057) +0.0115 +0.0168

(0.0060) (0.0083) +0.0121 +0.0157

(0.0067) (0.0082)

Note 1, 176 cements, Avg. = 0.0395, S.D. Note 2, 88 cements

*Coef./s.d. ratio less than 1.0.

0.04671

Table 12-27. Coefficients for equations for NAE cements relating the ratio of differences water storage divided by the percentage weight-loss of Series O concretes

Eq. No. Note Const. CaA C3S C4AF Si02 AUOs

1..

2_.

2A

2B

3..

4..

4A

4B

OWTR

s.d. OWTR

s.d. OWTR (odd)

s.d. OWTR (even)

s.d. OWTR

s.d. OWTR

s.d. OWTR (odd)

s.d. OWTR (even)

3.d.

= +0.178

= (0.037)

= +0.189

= (0.036) +0.153

= (0.048) +0.226

(0.058)

: -0.150

(0.141) -0.204

: (0.141)

: -0.325

(0.176) -0.141

^ (0.231)

+0.00347

(0.00114) +0.00223

(0.00121) +0.00279

(0.00167)

* +0.00176

(0.00182)

+0.00093

(0.00047) -0.00101

(0.00046) -0.00079

(0.00056) -0.00141

(0.00078)

+0.00215

(0.00147) +0.00241

(0.00148) +0.00579)

(0.00203)

* +0.00042

(0.00227) +0.00885 +0.0167

(0.00451) (0.0057) +0.01070 +0.0156

(0.00452) (0.0058) +0.01329 +0.0189

(0.00546) (0.0075) +0.00974 +0.0135

(0.00758) (0.0091)

Note 1, 164 cements, Avg. = 0.0454, S.D. = 0.04165 Note 2, 82 cements

*Coef./3.d. ratio less than 1.0. Table 12-28. Calculated contributions of independent vari- ables to OWTR, the ratio (ODRY -OWET)/ODRY for

Series O concretes made of AE + NAE cements

Inde- pendent

variables

Range of variables

(percent)

Coefficients from eq 2

table 12-26

Calculated

contributions

to OWTR

Calculated range of contributions to OWTR

Const. = +0.193 CaA** 1 to 15 +0.00199 +0.002 to +0.030 0.028 CsS 20 to 65 -0.00094 -0.018 to -0.061 0.043 OiAF**___ 1 to 16 +0.00257 +0.003 to +0.041 0.038 Na20 0 to 0.7 +0.0421 0 to +0.029 0.029 SO3** 1.2 to 3.3 -0.0187 -0.022 to -0.062 0.040 apf *2500 to 5500 -0.000027 -0.068 to -0.148 0.080 Loss** 0.3 to 3.3 +0.0102 +0.003 to +0.034 0.031 MgO 0 to 5 -0.0070 0 to -0.035 0.035

Air-content. _ 0 to 11 -0.0122 0 to -0.134 0.134 Cu 0 to 0.05 -0.795 0 to -0.040 0.040 SrO** 0 to 0.4 +0.0516 0 to +0.021 0.021

*cmVg.

**Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

associateci with decreases of the OWTR ratio. Increases of Na20 were possibly associated with

increases of the OWTR ratio. The coefficients for C3A, C4AF, Loss, and SrO were of doubtful significance.

5.4.2. Absorption Ratio for Series A Concretes

The frequency distribution of AWTR, the ratio

of (ADRY-AWET)/AWET, is presented in table

12-29. There was a broad distribution of values

and an overlapping of the values obtained with

the different types of cement.

Equations are presented in table 12-30 indi- cating the independent variables associated with

AWTR. Equation 1 indicates that an increase of the air content was associated with a decrease of the absorption ratio. (See also table 12-33.) The

60
differences between the percentage weight-loss on air drying and the percentage weightcretes to various independent variables OWTR = (ODRY - OWET)/ODRY

NajO SO3 APF Loss MgO

Air content Cu SrO S.D.

+0.0453

(0.0163) +0.0421

(0.0167) +0.0773

(0.0227)

* -0.0099

(0.0270) +0.0471

(0.0164) +0.0456

(0.0170) +0.0857

(0.0234)

* -0.0042

(0.0265)

-0.0148

(0.0097) -0.0187

(0.0097) -0.0313

(0.0156) -0.0137

(0.0130)

-0.000029

(0.000007) -0.000027

(0.000007) -0.000032

(0.000010) -0.000022

(0.000010) -0.000025

(0.000006) -0.000024

(0.000006) -0.000028

(0.000009) -0.000020

(0.000008)

+0.0098

(0.0055) +0.0102

(0.0054) +0.0095

(0.0082) +0.0109

(0.0076)

-0.0060

(0.0023) -0.0070

(0.0023) -0.0089

(0.0036) -0.0047

(0.0033)

-0.0122

(0.0015) -0.0122

(0.0015) -0.0113

(0.0021) -0.0139

(0.0022) -0.0127

(0.0015) -0.0128

(0.0015) -0.0126

(0.0022) -0.0138

(0.0021)

0.03473

-0.795

(0.322) -1.416

(0.476)

* -0.477

(0.480)

+0.0516

(0.0340) +0.0588

(0.0500) +0.0527

(0.0476)

0.03402

0.03417

0.03338

+0.00607

(0.00382) +0.00928

(0.00399) +0.01415

(0.00579) +0.00744

(0.00569)

0.03529

-0.740

(0.327) -1.284

(0.493) -0.571

(0.477)

+0.0386

(0.0343)

* +0.0250

(0.0494) +0.0552

(0.0481)

0.03480

0.03555

0.03380

between the percentage weight-loss on air drying and the percentage weight-gain with

to various independent variables OWTR = {ODRY - OWET)/ODRY

FejOs NajO SO3 APF Loss MgO

Air content Cu SrO S.D.

+0.0480

(0.0165) +0.0408

(0.0168) +0.0792

(0.0205)

* +0.0043

(0.0285) +0.0500

(0.0167) +0.0452

(0.0173) +0.0836

(0.0205)

* -0.0052

(0.0295)

-0.0152

(0.0098) -0.0199

(0.0097) -0.0240

(0.0144)

* -0.0134

(0.0141)

-0.000028

(0.000007) -0.000026

(0.000007) -0.000025

(0.000009) -0.000029

(0.000011) -0.000024

(0.000006) -0.000022

(0.000006) +0.000021

(0.000008) -0.000023

(0.000009)

+0.0127

(0.0056) +0.0141

(0.0055)

* +0.0061

(0.0086) +0.0184

(0.0079)

-0.0057

(0,0024) -0.0068

(0.0023) -0.0086

(0.0031) -0.0058

(0.0037)

-0.0150

(0.0038) -0.0136

(0.0037) -0.0156

(0.0055) -0.0122

(0.0056) -0.0162

(0.0038) -0.0151

(0.0038) -0.0147

(0.0055) -0.0151

(0.0056)

0.034

-0.728

(0.326) * -0.403

(0.457) -0.927

(0.477)

+0.0727

(0.0348) +0.0590

(0.0524) +0.0885

(0.0526)

0.033

0.030

0.035

+0.00489

(0.00389) +0.00810

(0.00410) +0.01923

(0.00561)

* +0.00079

(0.00592)

0.035

-0.661

(0.335)

* -0.344

(0.457) -0.729

(0.488)

+0.0538

(0.0355)

* +0.0328

(0.0483) +0.0894

(0.0541)

0.034

0.031

0.036

Table 12-29. Frequency distribution of cements with respect to AWTR, the ratio of the difference between weight-loss and weightgain divided by the weight-loss. AWTR = (ADRY -AWET)/ADRY

Absorption ratio

-0.15 -0.12 -0.09 -0.06 -0.03 0 +0.03 0.06 0.09 0.12 0.15 Type cement to to to to to to to to to to to Total -0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 0.12 0.15 0.18

Number of cements

I 1 3 2 6 7 24 21 11 4 79 lA 1 2 1 1 3 8

II 1 3 3 13 17 24 3 1 1 66 IIA 1 1 1 3

III 4 1 1 3 8 2 1 20

IIIA 2 1 3 IV, v.. 2 4 5 3 1 15

Total 2 1 10 11 11 30 57 50 16 5 1 194

61
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q q

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62
Table 12-32. Calculated contributions of independent vari- ables to AWTR, the ratio of (ADRY -AWET)/ADRYfor

Series A concretes made of AE -\- NAE cements.

Inde- pendent

variable

Range of variables

(percent)

Coeuicients from eq 3

table 1^—oU

L>alculatea contributions

to A W 1 K

Calculated range of contributions to AWTR

Const. = +0.0758

Air-content.. 0 to 13 -0.0056 0 to -0.073 0.073 CjAF**_._ 1 to 16 +0.00291 +0.003 to +0.047 0,044 NazO 0 to 0.7 +0.0651 0 to +0.046 0.046 APF *2500 to 5500 -0.000016 -0.040 to -0.088 0.048 MgO 0 to 5 -0.00597 0 to -0.030 0.030 Cu 0 to 0.05 -1.032 0 to -0.051 0.051 SrO 0 to 0.4 +0.0857 0 to +0.034 0.034

*cmVg.

**Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

Table 12-33. "F" values for significance of reduction of variance due to added variables

Critical "F" ratios Table Equations* "F" D.F.

ratio a = 0.01 a = 0.05

12-2 0,1 18.4 3:177 3.88 2.67

1,2 24.0 5:172 3.13 2.28

2,3 1.95 4:168 3.42 2.42

0,4 17.4 5:175 3.13 2.28

4,5 17.4 5:170 3.13 2.28

5,6 3.27 3:167 3.88 2.67 12—3 0,1 17.8 3:165 3.88 2.67

1,2 20.5 5:160 3.13 2.28

2,3 2.07 3:157 3.90 2.67

0,4 18.5 5:163 3.13 2.28

4,5 12.9 5:158 3.13 2.28

5,6 2.40 4:154 3.43 2.42

0,1 11.2 4:172 3.42 2.42

1,2 26.6 4:168 3.42 2.42

2,3 13.6 2:166 4.71 3.05

3,4 2.56 4:162 3.43 2.42

0,5 19.6 9:167 2.52 1.93

5,6 13.5 2:165 4.73 3.05

6,7 2.21 3:162 3.90 2.67 19—7 0,1 9.7 4:160 3.43 2.42

1,2 23.9 4:156 3.43 2.42

2,3 12.0 2:154 4.74 3.05

3,4 2.20 4:150 3.44 2.42

0,5 17.3 9:155 2.52 1.93

5,6 11.9 2:153 4.74 3.05

6,7 1.98 3:150 3.90 2.67 12-10 0,1 718 2:179 4.70 3.05

0,2 6.77 2:179 4.70 3.05

2,3 25.5 2:177 4.70 3.05

3,4 34.2 4:173 3.42 2.42

4,5 3.81 4:169 3.42 2.42

0,6 19.1 6:175 2.92 2.15

6,7 21.8 4:171 3.42 2.42

7,8 4.31 4:167 3.42 2.42 12-11 0,1 816 2:167 4.72 3.05

0,2 11.7 4:165 3.43 2.42

2,3 31.4 4:161 3.43 2.42

3,4 3.46 4:157 3.43 2.42

0,5 14.5 6:163 2.92 2.15

5,6 20.0 4:159 3.43 2.42

6,7 3.81 4:155 3.44 2.42 12-14 0,1 2.65 2:173 4.73 3.05

0,2 8.00 4:171 3.42 2.42

2,3 26.4 4:167 3.43 2.42

3,4 3.44 5:162 3.13 2.28

4,5 4.05 1:161 6.77 3.90

0,6 17.6 9:166 2.52 1.93

6,7 3.94 4:162 3.44 2.42

7,8 4.82 1:161 6.77 3.90 12-15 0,1 2.07 2:161 4.73 3.05

0,2 7.16 4:159 3.44 2.42

2,3 25.8 4:155 3.44 2.42

3,4 3.27 5:150 3.14 2.28

4,5 16.3 1:149 6.78 3.90

0,6 16.7 9:154 2.52 1.93

6,7 4.08 4:150 3.44 2.42

7,8 16.9 1:149 6.78 3.90

Table 12-33. "F" values for significance of reduction of variance due to added variables—Continued

Critical "F" ratios Table Equations* <<P" D.F.

ratio

oi — 0.01 Of = 0.05

12-18 0,1 22.6 2:175 4.72 o.UO

1,2 13.0 6:169 2.92 2.15

2,3 4.10 2:167 4.72 3.05

0,4 17.7 8:169 2.62 2.00

4 6 4 15 2*167 4.72 o.uo 12-19 0,1 4.18 2:163 4.73 o.UO

1.2 12.3 6:157 2.92

2,3 3.53 2:155 4.74 3.05

0,4 10.7 8:157 2.62 2.00

4,5 3.57 2:155 4.74 o.\)i> 12-22 0,1 9.59 5:168 0.13

1,2 2.81 5:163 3.13 2.28

2,3 7.69 1:162 6.77

0,4 8.11 6:167 2.92 2.15

4,5 3.33 4:163 3.43 2.42

5,6 7.69 1:162 6.77 12-23 0,1 5.76 5:156 0.14 2 28

1,2 3.25 5:151 3.14 2!28

2,3 6.87 1:150 6.78 3.90

0,4 4.89 6:155

4 5 3 93 4*151 3.44 0 AO

5)6 6!80 1:150 6.78 3.90 12-26 0,1 15.2 10:166 2.93 1.90

1,2 4.50 2:164 4.72 3.05 0 3 19.9 7*169 2.75 2.07

3)4 3!40 2:167 O.UO 12-27 0,1 8.70 10:154 2.93 1.90

1,2 5.15 2:152 4.74 3.05

0,3 10.4 7:157 2.75 2.07 3 4 3.37 2 '155 A '7A 4. 1

4

3.05 12-30 0,1 5.19 2:173 4,7Z O.05

1,2 5.44 5:168 3.13 2.28

0,3 6.58 8:167 2.62 2.00

0,4 6.12 6:169 2.92 2.15

4,5 6.72 2:167 4.72 3.05 12-31 0,1 1.98 2:161 4.73 3.05

1.2 6.08 5:156 3.13 2.28

0,3 5.84 8:155 2.62 2.00

0,4 5.44 6:157 2.92 2.15

4,5 6.04 2:155 4.74 3.05

*0 in the equation column refers to the S.D. value of the corresponding dependent variable as given in footnotes in the tables of equations.

use of other commonly determined variables, C3A,

C4AF, Na20, APF, and MgO, in eq 2 resulted in a further significant reduction in the S.D. value.

The S.D. values of eqs 2 and 3 cannot be compared because of the absence of C3A in eq 3, but,

judging from eqs 4 and 5, it appears likely that

the inclusions of Cu and SrO with the commonly

determined variables caused a significant reduction of variance. (See table 12-33.)

The coef./s.d. for Fe203 in eq 4 was less than

1.0, but in eq 5 the ratio was greater than 1.0. In eqs 3A and 5A the coef./s.d. ratios for C4AF,

Fe^Oa, MgO, and SrO were less than 1.0 with the

smaller lot of cements.

A corresponding series of equations for the NAE

cements is presented in table 12-31. The use of

the air content in eq 1 did not result in a significant reduction of the S.D. value. (See table 12-33.) In eqs 3B and 5B the coef./s.d. ratio for the air- content of the NAE cements was less than 1.0 with the smaller groups of cement. The coefficients of the other independent variables were consistent

with those of the p.-evious table where the AE

cements were included.

63
Using the coefficients of the independent variables of eq 3, table 12-30, and the ranges of these

variables, computations were made of the calculated contributions to AWTR. These estimated

contributions and the calculated ranges of the

contributions are presented in table 12-32. Increases in air content and possibly fineness, MgO,

and Cu were associated with decreases of the

AWTR ratio. Increases of Na20 and possibly SrO

were associated with increases of the AWTR ratio.

Table 12-34. Coefficients, coef./s.d. ratios, and calculated ranges of contributions to percentage loss of weight on drying, percentage gain of weight on resoaking, and ratios for Series 0 concretes made of NAE cements

Column 1 2 3 4

Eq. No. 3 4 3 2

Table No. 12-3 12-11 12-19 12-27

Dependent variables ODRY OWET ORWT OWTR

Constant +4.233 +3.813 +0.849 +0.189

Air content, coef. +0.0846

2.7 0.38

+0.1128

3.9 0.51

+0.0124

3.0 0.056 -0.0020

1.7 0.028

-0.0136

3.7 0.061 +0.00223

1.8 0.031 -0.00101

2.2 0.045 +0.00241

1.6 0.034 +0.0408

2.4 0.029

Coef./s.d Calculated range

Coef./s.d Calculated range

CaS, coef -0.02265

6.6 1.02 +0.03474

3.6 0.49 -0.5362

4.0 0.38 -0.6471

5.6 0.71 -0.2549

3.8 0.51

-0.01931

6.3 0.87 +0.03057

3.3 0.43 -0.6766

5.7 0.47 -0.6138

5.8 0.68 -0.1836

3.0 0.36

Coef./s.d Calculated range CiAF, coef -0.00319

2.0 0.045 -0.0653

3.7 0.046

Coef./s.d Calculated range NajO, coef. Coef./s.d Calculated range KjO, coef Coef./s.d Calculated range

SO3, coef. -0.0199

2.1 0.040 -0.0068

3.0 0.034 +0.0141

2.6 0.042 -0.000026

3.7 0.078

Coef./s.d Calculated range +0.00611

2.3 0.030 -0.0125

2.1 0.038 +0.0000429

6.8 0.120

Coef./s.d

-0.0573

1.3 0.17

-0.0682

1.8 0.20 Coef./s.d Calculated range APF, coef

Ba, coef +0.923

1.5 0.18

+0.8131

1.4 0.16 +4.606

2.0 0.23

Coef./s.d Calculated range Cu, coef +0.665

1.8 0.33 -0.0441

1.8 0.044

-0.728

2.3 0.036

Coef./s.d Calculated range Mn, coef Coef./s.d Calculated range -16.49

1.3 0.16

-19.28

1.8 0.19 SrO, coef -0.0727

2.1 0.029Coef./s.d Calculated range -0.657

1.2 0.33

-0.8397

1.8 Calculated range 0.42

.

.

64
6. Discussion

6.1. Variables Associated With Weight-Loss,

Absorption, and Their Ratios

A series of equations selected from those pre- viously given in tables for concretes made with

NAE cements is presented in tables 12-34 and

Table 12-35. Coefficients, coef./s.d. ratios, and calculated ranges of contributions to the percentage loss of weight on drying, the percentage gain of weight on resoaking, and ratios for Series A concretes made of NAE cements

12-35 in order that the variables, their coefficients,

and the possible range of contributions to the dependent variables may be compared more readily.

The equations are presented vertically instead of horizontally as in previous tables of this section.

Reference is also made to the equations for the

Column

Eq. No.

Table No.

Dependent variable

Constant

Air content, coef—

Coef./s.d Calculated range.

w/c, coef Coef./s.d Calculated range.

CsA, coef Coef./s.d Calculated range.

CsS, coef - - - Coef./s.d Calculated range .

C<AF, coef Coef./s.d Calculated range.

NasO, coef

Coef./s.d Calculated range.

KjO, coef

Coef./B.d Calculated range.

SO3, coef Coef./s.d Calculated range. MgO, coef Coef./3.d Calculated range. APF, coef

Coef./3.d Calculated range.

Loss, coef Coef./s.d Calculated range.

Ba, coef Coef./s.d Calculated range.

Co, coef

Coef./s.d Calculated range.

Cu, coef Coef./s.d Calculated range. Rb, coef Coef./s.d Calculated range.

SrO, coef

Coef./s.d Calculated range.

V, coef Coef./8.d Calculated range.

Zr, coef Coef./8.d... Calculated range.

12-7 ADRY

-1.069

-1-0.0646

1.9 0.29

-1-7.864 4.8 1.18

-t-0.02282 2.4

0.32 -0.02216

6.7 1.00

-1-0.05101 4.4 0.71 -0.58B7

4.6 0.41 -0.6948

5.8 0.76 -0.2511

3.5 0.50

-0.0824

2.0 0.25

-1-1.043 1.7 0.20

-f3.748

1.5 0.19 -12.31

1.0 0.12

-0.6953

1.3 0.35

6

12-15 AWET

-1-0.560

-1-5.047 4.1 0.76

-1-0.01921 2.0 0.27 -0.0190

5.8 0.86

-1-0.03078 2.8 0.43 -0.7028

5.7 0.49 -0.6713

6.0 0.74 -0.1648

2.4 0.33

-0.0743

1.9 0.22

-1-1.287 2.1 0.25

-1-19.71 1.3 0.19

-1-6.973 2.7 0.40

-0.7586

1.6 0.38

2

12-23 ARWT

-1-0.921

-1-0.00769

1.8 0.035

-0.00273

1.7 0.038 -0.0653

3.1 0.046

-1-0.00509

1.7 0.025

-1-0.0000159

2.3 0.048

-1-0.190 1.7 0.004

-1-0.958 2.4 0.048

-0.0865

2.2 0.035 -0.306

1.5 0.031

8

12-31 AWTR

-1-0.0904

-0.00787

2.0 0.035

-1-0.00274

1.7 0.038

-1-0.0673 3.2 0.047

-0.00527

1.8 0.026 -0.0000191

3.0 0.057

-1.007

2.5 0.050

-1-0.0800 2.0 0.032

65
concretes made of AE + NAE cements which

have previously been presented.

The variables associated with the percentage

loss of weight when the specimens were dried in

air for 56 days (col 1) were generally, but with a few exceptions, also associated with the percentage weight-gain when the dried specimens were

later placed in water for 28 days (col 2). Higher air contents of the concretes were asso- ciated with higher values for weight-loss with

air-drying and greater absorption on rewetting

for the Series 0 concretes but not the Series A

concretes. When the AE cements were included

in the computation, the coef./s.d. ratio of the "air

content" was greater. See eq 3 table 12-2 and

eq 5 table 12 10. Concretes made with NAE cements, which re- quired a higher water/cement ratio to achieve the

desired slump, also had higher weight-loss and

absorption in drying and wetting, as shown by

the coefficients for w/c in table 12-35, cols. 1 and 2. Of the major potential compounds, higher C3A

was probably associated with higher loss on drying and gain on rewetting with the Series A concretes, but not with the Series 0 concretes. Higher

Table 12-36. Relationships of weight loss and weight gain of concretes to dynamic Young's modulus of elasticity (in psi X 10"^)

of concretes at H, 70, and 98 days

S.D. "F" ODRY

3.d. = +6.10 - 0.723 = (0.29) (0.060) OD14 0.30 72 ODRY

s.d. = +5.42 - 0.624 = (0.27) (0.060) OD70 0.32 54 ODRY

3.(1. = +5.25 - 0.510 = (0.48) (0.095) OD98 0.37 14.5 OWET

s.d. = +6.26 - 0.775 = (0.24) (0.051) OD14 0.26 114 OWET

s.d. = +5.41 - 0.643 = (0.24) (0.054) OD70 0.29 71 OWET

s.d. = +5.76 - 0.628 = (0.43) (0.085) OD98 0.33 27 ADRY

s.d. = +6.12 - 0.720 = (0.37) (0.078) AD14 0.33 43 ADRY

s.d. = +5.27 - 0.583 = (0.33) (0.075) AD70 0.34 30 ADRY

s.d. = +4.64 - 0.384 = (0.62) (0.122) AD98 0.39 5.00 AWET

s.d. = +6.07 - 0.731 = (0.34) (0.071) AD14 0.30 53 AWET

s.d. = +5.16 - 0.580 = (0.31) (0.070) AD70 0.32 35 AWET

s.d. = +4.96 - 0.467 = (0.58) (0.131) AD98 0.36 8.49 ODRY

s.d. = +8.20 - 1.151 = (0.33) (0.067) 0D14 0.25 146 ODRY

s.d. = +6.18 - 0.786 = (0.32) (0.070) OD70 0.31 63 ODRY

s.d. = +7.67 - 0.978 = (0.76) (0.148) OD98 0.36 22 OWET

s.d. = +7.72 - 1.074 = (0.30) (0.061) 0D14 0.23 152 OWET

s.d. = +5.76 - 0.719 = (0.30) (0.065) OD70 0.29 60 OWET

s.d. = +7.23 - 0.913 = (0.70) (0.136) OD98 0.22 22 ADRY

s.d. = +8.01 - 1.103 = (0.35) (0.073) AD14 0.26 115 ADRY

s.d. = +6.00 - 0.738 = (0.34) (0.077) AD70 0.32 46 ADRY

s.d. = +6.79 - 0.798 = (0.74) (0.144) AD98 0.37 15 AWET

s.d. = +7.61 - 1.042 = (0.34) (0.072) AD14 0.26 106 AWET

s.d. = +5.71 - 0.699 = (0.33) (0.075) AD70 0.32 44 AWET

s.d. = +6.64 - 0.790 = (0.71) (0.138) AD98 0.35 16

9...

10.

11_

12.

13.

14_

15.

16.

17 _

18.

19.

20-

21.

22.

23.

24.

Equation Type cement

AE +NAE

NAE

66
CaS was associated with lower loss on drying and

lower absorption when rewetted for both series. Higher C4AF was associated with higher loss on

drying and higher absorption for both series. The coefficients for Na.O and K2O were highly

significant in both drying and wetting for both

series of concretes. Increases of the alkalies were

associated with decreases of the loss of weight on

drying and gain of weight on rewetting. Of the

two alkalies, only Na20 had a significant effect on the ratios ORWT and OWTR.

An increase of the SO3 content in both series was associated with a decrease of the weight-loss

or weight-gain but not with the ratios. However,

an increase of fineness was not associated with the

loss of weight or weight-regain when rewetted,

but was associated with the ratios ORWT,

OWTR, and AWTR.

Of the various trace elements, Cu had coef./s.d.

values of 2.0 or greater with 5 of the 8 equations.

SrO had coef./s.d. ratios of 2.0 or slightly over in some of the ratios (see columns 3 and 4 of tables

12-34 and 12-35.) Other trace elements usually

had coef./s.d. values less than 2.0 and were,

therefore, of doubtful significance.

6.2. Weight-Loss and Absorption Versus

Dynamic Modulus of Elasticity

Table 12-36 shows linear equations indicating

the relationship between the dynamic modulus of

elasticity at 14, 70, and 98 days total age and the

percentage loss of mositure during 56 days of

drying and the percentage absorption with the

subsequent 28 days in water. The independent

variables, ODRY, OWET, ADRY, and AWET,

as indicated previously are the weight-loss and

weight-gain of the 6- X 8- X 16-in concrete

blocks. The independent variables represent dynamic modulus values obtained from measure- ments of fundamental flexural frequencies of companion 3- X 4- X 16-in concrete beams made

from the same concrete mixes as the blocks. 0D14

and AD14 refer to the dynamic modulus after 14 days of moist curing; OD70 and AD70 to dynamic modulus of the same beams after 56

days of drying in laboratory air (total age 70

days); and OD98 and AD98 to dynamic modulus

after 28 days soaking in water (total age 98 days).

The initial 0 and A, respectively, refer, as with

other symbols, to the Series 0 concretes with

constant w/c ratio and Series A concretes with

constant slump.

The reduction of variance was greater when

the loss or gain of weight was related to the values

for dynamic modulus after 14 days moist curing.

This was found for both the Series 0 and Series

A concretes each made of AE + NAE or NAE

cements. Higher dynamic modulus was significantly related at all ages and conditions of test to lower loss of weight with drying and lower

absorption when rewetting.

6.3. Air Content Versus Absorption and

Weight-Loss

As indicated in subsection 6.1 as well as in the

various equations of this section, higher air contents of the concretes were associated with higher

weight-loss on drying and higher weight-gain when

placed in water. It was previously indicated in

section 10, tables 10 1 and 10-2, and in the dis- cussion in subsection 6.1 of section 10 that concretes made with air-entraining cements had

lower cement contents than the original design

mix and most of the concretes made with nonair-entraining cements. The somewhat leaner and more porous nature of the concretes made with

the air-entraining cements may therefore have

been responsible for the higher weight-loss and

absorption. However, as indicated in section 11 on durability in subsection 6.3, the saturation

ratio after 24 hours in water was lower with higher

air contents. The longer period (28 days versus 24 hours) in water may also have been responsible

for the differences in these two series of tests.

7. Summary and Conclusions

Concrete specimens 6- X 8- X 16-in (approx.

15- X 20- X 40-cm) were made from 199 portland

cements of different types, using 5^2 bags of cement per cubic yard (approx. 307 kg/m^). In one series, the water-cement ratio was constant

at 0.635, and in the other, the water was adjusted,

if necessary, to obtain a slump of 5 ± 1 in (12.7

j + 2.5 cm). Specimens were moist cured for 14

1 days, dried in laboratory air for 56 days, and then

j immersed in water for 26 days. Determinations

I were made of the percentage weight-loss and the

percentage absorption, and various ratios were

calculated for the weight-loss and weight-gain.

The observations and conclusions were as follows:

I (7.1) The percentage loss of weight as a result

of drying in laboratory air ranged from less than

!| 2.0 to more than 4.0 percent.

(7.2) When the air-dried specimens were later immersed in water for 28 days the absorption

ranged from less than 2.0 up to 4.0 percent. There was a highly significant relationship between the

loss on drying and the subsequent absorption.

(7.3) The ratio of weight-gain to weight-loss

ranged from about 0.8 to 1.2 and the ratio

of (ODRY -OWET)/ODRY ranged from about — 0.15 to +0.18 with similar values for the A

Series.

(7.4) The frequency distributions of the

weight-loss, weight-gain, and the two ratios indicated that a range of values was obtained for each

of the types of cement, and that there was considerable overlapping of the values obtained for the different types.

(7.5) Computations of equations by a least67
squares method were used to determine the

chemical and physical properties of the cements

which were associated with the weight-loss, the

weight-gain, and the ratios of gain to loss. The

equations ware computed for all cements for which

minor constituents and trace elements had been

determined. Equations were computed for the

AE + NAE cements and for the NAE cements.

The equations were computed using the calculated major potential compounds or the major

oxides together with other commonly determined

variables, and then with trace elements which

appeared to have a significant effect. The following observations relate to the Series

0 concretes made of NAE cements as summarized

in table 12-34:

(7.5.1) Increases of C4AF and possibly air content were associated with increases of ODRY,

the percentage loss of weight on drying. Increases

of C3S, Na20, K2O, and SO3 were associated with

decreases of the loss of weight on drying.

(7.5.2) Increases of the air content, C4AF,

and possibly Cu were associated with increases of OWET, the percentage weight-gain when the air- dried specimens were immersed in water for 28

days. Increases of C3S, Na^O, K2O, and SO3 were

associated with decreases of the weight-gain.

(7.5.3) Increases of air content and fineness,

and possibly MgO, were associated with increases

of ORWT, the ratio OWET/ODRY. Increases of Na20, and possibly C4AF and Loss, were associated with decreases of ORWT. Of these, variations of fineness had the greatest calculated effect. (7.5.4) Increases of air content, fineness, MgO,

and possibly C3S, Cu, and SrO, were associated

with decreases of OWTR, the ratio (ODRY

-qWET)/ODRY. Increases of NasO and loss on

ignition were possibly associated with increases

of the OWTR ratio.

(7.6) The independent variables associated

with the dependent variables of the Series A

concretes (where the water was adjusted to obtain a selected slump) were in general agreement with

those of the constant water/cement ratio concretes.

(7.7) The use of the major oxides instead of the calculated potential compounds as independent variables (together with other commonly determined variables) resulted in equations with

similar estimated standard deviation values.

(7.8) Of the various trace elements, the coefficients for Cu and SrO were probably significant

in equations for some of the properties. Other

trace elements, though appearing in the equations, were of doubtful significance.

8. References

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

and Concrete, Revised Edition, (Edward Arnold

Ltd., London, p. 347, 1956).

[2] Interrelations Between Cement and Concrete Properties, Part 1 —Section 1, Materials and techniques,

Blaine, R. L., Arni, H. T., and Foster, B. E.; Section

2, Water requirements of portland cements, Blaine, R. L., Arni, H. T., and Clevenger, R. A.; Section 3, Occurrence of minor and trace elements in portland

cements, Blaine, R. L., Bean, Leonard, and Hubbard,

Elizabeth K.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 2, 40 pages (Aug. 1965).

[3] Interrelations Between Cement and Concrete Properties, Part 2—Section 4, Variables associated with

expansion in the potential sulfate expansion test, Blaine, R. L., Arni, H. T., and Evans, D. N.; Section

5, Heat of hydration of portland cements, Elaine,

R. L., and Arni, H. T.; Section 6, Variables associated with small autoclave expansion values of portland

cements, Blaine, R. L. and Arni, H. T.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 5, 46 pages (July 1966).

[4] Interrelations Between Cement and Concrete Properties, Part 3—Section 7, Compressive strength of mortars, Blaine, R. L., Arni, H. T., and DeFore,

M. R.; Section 8, Compressive strength of steam- cured portland cement mortars, Blaine, R. L., Arni, H. T., and DeFore, M. R.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 8, 101 pages (Apr. 1968).

[5] Interrelations Between Cement and Concrete Properties, Part 4—Section 9, Shrinkage of hardened port- land cement pastes, Blaine, R. L., Arni, H. T., and

Evans, D. N.; Section 10, Shrinkage and expansion

of concretes, Blaine, R. L., and Arni, H. T.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 15, 78 pages (Mar. 1969).

68
Section 13. Dynamic Young's Modulus of Elasticity of Concrete

R. L. Blaine and H. T. Arni

The relationships between cement characteristics and dynamic Young's modulus of elasticity of concretes at different ages and moisture conditions were studied by computing

multivariable regression equations with the aid of a digital computer. An increase of the air- content and water/cement ratio needed for the desired slump were associated with a decrease

of the dynamic E. Increases in C3S and SO3 were associated with increases of the dynamic E. Other independent variables, although significant, generally had less effect on the dynamic E. The use of trace elements as independent variables in equations resulted in a significant re- duction of variance when the concrete specimens were moist. There was generally a decrease

of dynamic modulus when moist specimens were dried in laboratory air for 4 or 8 weeks and

an increase when the air-dried specimens were resaturated. Placing the air-dried specimens in water for 24 hours resulted in a slight decrease in dynamic modulus with some concretes and

an increase with other concretes. Key words: Cement composition; compressive strength; concrete; dynamic modulus of elasticity; effect of moisture on dynamic E; modulus of rupture; portland cement; trace elements. Contents

Page Introduction 69

Materials 70

2.1. Cements 70

2.2. Aggregates 70 Methods of Test 70

3.1. Preparation of concretes 70

3.2. Test specimens 70

3.3. Storage of test specimens 70

3.4. Measurement of specimens 70 Abbreviations 70

Statistical analyses 71 Results of tests 71

6.1. Dynamic modulus after 14 days moist curing 71

6.1.1. Dynamic modulus of Series 0

concretes 71

6.1.2. Dynamic modulus of Series A

concretes 74

6.2. Dynamic modulus after 28 days drying 75

6.2.1. Dynamic modulus of Series 0

concretes 75

6.2.2. Dynamic modulus of Series A ^ concretes 75

6.3. Dynamic modulus after 56 days drying 80

6.3.1. Dynamic modulus of Series 0

concretes 80

6.3.2. Dynamic modulus of Series A

concretes 81

6.4. Dynamic modulus after 28 days resoaking. _ 83

6.4.1. Dynamic modulus of Series 0

concretes 83

6.4.2. Dynamic modulus Of Series A 8. concretes 85 9.

Page

6.5. Effect of drying on dynamic modulus 88

6.5.1. Ratio of OD70 to 0D14 for Series 0

concretes (OE70/14) 88

6.5.2. Ratio of AD70 to AD14 for Series A

concretes (AE70/14) 91

6.6. Effect of rewetting on dynamic modulus 95

6.6.1. Ratio of 98-day (wet) to 70-day (dry)

dynamic modulus of Series O

concrctGs 95

6.6.2. Ratio of 98-day (weV)Vo"76-day (dry)

dynamic modulus of Series A

concretes 97

6.7. Effect of 24 hours water storage of air-dried concrete on dynamic modulus 97

6.7.1. Ratio of 71-day (24 hr water storage)

to 70-day (air-dried) dynamic

modulus of Series 0 concretes 97

6.7.2. Ratio of 71-day (24 hr water storage)

to 70-day (air-dried) dynamic

modulus of Series A concretes 100 Discussion 109

7.1. Independent variables associated with the dynamic modulus of elasticity 109

7.2. Effect of trace elements 109

7.3. Relationships of dynamic modulus to various

characteristics of mortar bars 112

7.4. Compressive and flexural tests of concretes., 112

7.5. Effect of drying and resoaking on dynamic

modulus of concretes 113 Summary and conclusions 124 References 125

1. Introduction

Modulus of elasticity determined by resonant

frequency methods has been used to study the

effects on concrete properties of various treat- ments, conditions, or changes in conditions [1, 2,

3", 4].i Examples of such use include: (1) deterio-

' Figures in brackets refer to literature references at the end of this

j section (p. 125).

ration due to freezing and thawing in laboratory

tests [5, 6] ; (2) deterioration due to natural weathering [7]; (3) effect of chemical attack [8]; (4) effects of incomplete consolidation [9]; (5) effect of curing methods [10]. Also various studies have

been made in an attempt to relate dynamic (modulus to other properties of the concrete such as

static modulus of elasticity, creep, relaxation.

69
shrinkage, and compressive, flexural, and tensile

strength [11, 12, 13, 141. The object of this paper i.^- to investigate the

effect on dynamic modulu:. u^iiler various conditions of curing, drying, and t ewetting of variables

connected with the cements used. The source and

amount of aggregate was the same throughout

the study. The cement content was held constant,

ejs ept for changes required by the amount of

entrained air. Dynamic modulus tests were con- ducted according to ASTM Designation C 215

[15].

2. Materials

2.1. Cements

The cements used in the present tests were the same as those used in the work reported through - out the series of sections of the Interrelation Between Cement and Concrete Properties. The

results of chemical analyses and the semiquantitative spectrochemical analyses were presented in

sections 2 and 3 of part 1 of this series of articles

[16]. Reports of other properties of these cements,

mortars, and concretes have been presented in parts 2, 3, 4 [17, 18, 19], and in the first two sections of the present part 5. Most of the 199

Portland cements were obtained from different areas of the United States, but a few were obtained from other countries.

2.2. Aggregates

A high quality rounded quartzite coarse aggregate was used with a sand from the same source. The sand and coarse aggregate gradation was

previously presented in section 1 [16].

3. M. thods of Test

3.1. Preparation of Concretes

The details of the proportioning and mixing of the concretes were described in part 1, section 1 of this series of articles [16]. Two senes of concretes were made with these cements; one (P-ries

0) was made using a water/cement (w/c) ratio of 0.635, and the other (Ser]:-s A) with the water

varied, if necessary, to give a concrete with a

5 + 1-in slump. The concrete mix was designed

to contain 5.5 bags of cement per cubic yard but

varied somewhat as indicated in section 11 because

of the amount of entrained air.

3.2. Test Specimens

The 3- X 4- X 16-in concrete specimens of the

two series were made from the same batches of concrete used for the shrinkage and expansion

tests [19], the durability tests, and the weight-loss

and weight-gain tests reported in sections 11 and

12 of this publication.

3.3. Storage of Test Specimens

The concrete was cured at 73 + 1 °F in the

molds under damp burlap for the first 20 to 24

hours, then placed in a fog room at 100 percent

relative humidity until 14 days old. The specimens were then placed on end and exposed to laboratory

air at 73 °F and 50 percent relative humidity for

8 weeks. The specimens were then placed in water

for an additional 4 weeks.

3.4. Measurements of Specimens

The fundamental transverse frequencies of the

concrete specimens were determined in accordance

with ASTM Method C 215 [15]. The measure- ments were made on two 3- X 4- X 16-in prisms of each of the two series of concretes at 14 days

(after moist curing), at 70 days (after 8 weeks of drying in laboratory air), at 71 days (after 24

hours in water), and at 98 days (after 4 weeks

in water).

4. Abbreviations

The abbreviations, notations, etc., used in this

section for physical and chemical properties of the

cements are the same as those used in previous

sections of this series of articles. ^ In this section, as in the previous three, the

prefix "0" of the four-letter titles for the various

dependent variables refers to the concretes of Series 0 in which a water/cement (w/c) ratio of

2 These abbreviations include the use of CaA, CjS, C2S, and C4AF for the calculated potential compounds, tricalcium aluminate, tricalcium

silicate, dicalcium silicate, and tetracalciura aluminoferrite, respectively. Also used are Insol for insoluble residue, Loss for loss on ignition, APF for

air permeability fineness, Wagn for Wagner Turbidimeter fineness. AE +

NAE refers to air-entraining plus non-air-entraining cements, and NAE

to the non-air-entraining cements.

0.635 was used. The prefix A refers to the Series A

concretes which had a 5 + 1-in slump. A summary

of other titles for the dependent variables used in this section are as follows:

For Series 0 concretes made with a w/c of 0.635

0D14 = dynamic modulus in psi X 10"" at 14

days after moist curing.

OD42 = dynamic modulus in psi X 10"^ after

14 days moist curing followed by 28

days drying in laboratory air. OD70 = dynamic modulus in psi X 10"^ after

14 days moist curing followed by 56

days drying in laboratory air.
0D71 = dynamic modulus in psi X 10-'' after

air dried specimens had been placed

in water for 24 hours.

OD98 = dynamic modulus in psi X 10~"^ after

air dried specimens had been in water

for 28 days.

OE 70/14 = OD70/OD14

OE 98/70 = OD98/OD70

OE 71/70 = OD71/OD70

For Series A concretes having a 5 + 1-in slump,

the letter "A" is used instead of "0", as AD14,

AD42, AD70, AD71, AD98, AE 70/14, AE 98/70,

and AE 71/70 for the different independent variables. The values for dynamic Young's modulus of

elasticity will generally be referred to as dynamic

modulus, or dynamic E.

5. Statistical Analyses

The statistical techniques used to find and

evaluate the independent variables associated with

the dynamic modulus at the various ages and test conditions and the ratios of these values have

been described in a previous section of this series part 1, section 1, Materials and Techniques [16]. The statistical treatment was the same as that

used in all previous sections of this series of articles. Multiple regression equations were calculated by a least-squares method using various

independent variables to determine which showed

an association with each of the dependent variables. As in previous sections, equations were

calculated for both the AE + NAE cements and

the NAE cements. Calculations were made using

only commonly determined variables and also

using these together with minor and trace ele- ments.

After equations had been developed in which

independent variables showed significant relationships with the dependent variable, the residuals

of these equations were fitted by a least-squares

method to other independent variables and the

reduction in variance calculated. If any of the

additional independent variables indicated a significant reduction in variance, they were tried in the equation and retained if the coef./s.d. ratio was greater than 1.0.^ Ratios of reduction in variance to original vari- ance ("F" ratios) obtained by fitting equations were calculated for two kinds of cases: (1) for

' statistical terms and notations employed in this section are the same

as those used in previous sections of this series of articles. For example,

S.D. refers to the estimated standard deviation calculated from the resid- uals of a fitted equation, or the estimated standard deviation about the

average. Also, as in previous sections, s.d. refers to the estimated standard

deviation of a coefficient of an independent variable used in a fitted equation. The term coef./s.d. is the ratio of the estimated coefficient (of an

independent variable used in an equation) to its estimated standard

deviation. "F" designates Fisher's ratio of variances and D.F. is used to designate the number of degrees of freedom. As indicated in previous

sections, a coef./s.d. ratio greater than 1.0 was considered to be of sufficient signilRcance to warrant further investigation.

equations including a few main independent variables as compared to the original data on the

dependent variable, or (2) for equations in which

additional independent variables were included as compared to a previous equation with fewer

variables. The calculated "F" ratios and the

critical "F" values which must be equaled or exceeded for significance at the a = 0.05 and a =

0.01 levels are summarized in a table (table 13-57).

Equations were also calculated for the "odds"

and "evens" in the array of cements. Comparisons

were made of the coefficients of the variables in the two gi'oups of data and these were compared

to the coefficients and coef./s.d. ratios computed

for all the cements.

Although dynamic modulus of elasticity was

determined for both series of concretes made of

all of the 199 cements, the calculations of equations presented in this section were limited to those cements for which trace-element determinations had been made.

Equations presented in this section were selected

from a large number of trial equations indicating

the calculated relationship of various variables to the dynamic modulus values or their ratios.* A

summary of the relationships indicated by the

equations for both series of concretes is given in the discussion in subsection 7. Some of the limitations on interpretation of multivariable regression equations as well as other

statistical techniques used in this series of articles have been discussed in section 1, subsections 4.2,

4.3, and 5 [16]. Other limitations and problems of interpretation have also been discussed in other

sections of this series of articles.

* These equations were selected primarily to indicate the association with commonly determined independent variables having coef./s.d. ratios greater than 1.0 when used in multivariable equations, and also to indicate which of minor and trace elements may show a significant relationship.

6. Results of Tests

6.1. Dynamic Modulus After 14 Days Moist

Curing

6.1.1. Dynamic Modulus of Series O Concretes

The frequency distribution of the dynamic

moduli of the Series 0 concretes after 14 days

moist curing is presented in table 13-1. There

was a broad distribution of values and an over- lapping of the values for the different types of cement. The air-entraining cements (Types lA,

IIA, and IIIA) generally had values in the lower

half of the distribution curve. Equations are presented in table 13-2 indicating

the variables associated with the dynamic modulus of Series 0 concretes made of AE + NAE

71
Table 13-1. Frequency distribution of cements with respect to ODlIf, the dynamic modulus of elasticity of Series O concretes

after H days moist curing

Dynamic modulus of elasticity, 10' psi

3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 Type CGiHGnt to to to to to to to to to to to Total

3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6

Number of cements

I 1 3 16 34 24 3 1 82

868

320

315

lA 2 3 3

II 1 1 1

1 131 17 25 9 1 IIA 1 III 2

13

4 10 4 IIIA 12

1 IV, V 1 4 2 2 1

Total . 3 4 7 1 8 19 39 65 44 8 1 199

Table 13-2. Coefficients for equations relating ODl^, the dynamic Young's modulus of NAE cements, to various

Note 10" psi Const. Air content CsA CaS C4AP CaO ODU

s.d. = +3.767 = (0.173) -0.1622

(0.0078) 0D14

s.d. = +3.723 = (0.170) -0.1593

(0.0077) ODU (odd)

s.d. = +8.718 = (0.248) -0.1562

(0.0108) 0D14 (even)

s.d. = +3.811 = (0.249) -0.1646

(0.0116) ODU

s.d. = +1.978 = (2.492) -0.1621

(0.0078) 0D14

s.d. = +1.681 = (2.504) -0.1592

(0.0077) ODU (odd)

s.d. = +1.615 = (3.817) -0.1562

(0.0109) 0D14 (even)

s.d. = +0.735 = (3.621) -0.1643

(0.0116)

+0.00965

(0.00585) +0.01007

(0.00584)

* +0.00332

(0.00850) +0.01558

(0.00852)

+0.0194

(0.0022) +0.0196

(0.0021) +0.0193

(0.0028) +0.0190

(0.0036)

-0.0196

(0.0075) -0.0178

(0.0074) -0.0236

(0.0106) -0.0124

(0.0109) +0.0975 -0.1306

(0.0272) (0.0288) +0.1009 -0.1298

(0.0274) (0.0286) +0.1003 -0.1267

(0.0411) (0.0418) +0.1098 -0.1164

(0.0403) (0.0433)

*Coef./s.d. ratio less than one. Note 1, 180 cements, Avg. = 4.75 X 10» psi, S.D. = 0.3550 X 10^ psi Note 2, 90 cements

Table 13-3. Coefficients for equations relating ODU, (he dynamic Young's modulus

cements, to various

Note 10« psi Const. Air content CaA C^AF CaO ODU

s.d. = +3.691 = (0.171) -0.1328

(0.0195) ODU

s.d. = +3.618 = (0.176) -0.1346

(0.0193) OD14 (odd)

s.d. = +3.634 = (0.262) -0.1344

(0.0321) OD14 (even)

s.d. = +3.603 = (0.258) -0.1369

(0.0252) ODU

s.d. = +4.377 = (1.174) -0.1321

(0.0196) ODU

s.d. = +2.249 = (2.593) -0.1348

(0.0194) 0D14 (odd)

s.d. = +4.213 = (4.480) -0.1351

(0.0316) 0D14 (even)

s.d. = +4.081 = (3.414) -0.1367

(0.0254)

+0.00947

(0.00590) +0.01056

( 0.00596) +0.01025

(0.00946) +0.01004

(0.00824)

+0.0193

(0.0022) +0.0197

(0.0022) +0.0197

(0.0030) +0.0193

(0.0036)

-0.0168

(0.0075) -0.0144

(0.0075)

* -0.0096

(0.0127) -0.0193

(0.0099) +0.0721 -0.155

(0.0141) (0.022) +0.0947 -0.137

(0.0284) (0.029) +0.1621 -0.077

(0.0483) (0.047) +0.0737 -0.151

(0.0386) (0.041)

*Coef./8.d. ratio less than one. Note 1, 168 cements, Avg. = 4.820 X lO^ psi, S.D. Note 2, 84 cements

0.2585 X 10» psi

72
cements. The use of commonly determined variables, air content, C3A, C3S, C4AF, SO3, NazO,

K2O, and MgO in eq 1 resulted in a highly significant reduction in variance. (See table 13-57,^

p. 108).

Using thjese commonly determined variables in eq 2 together with the trace elements Mn, Rb,

and Zr which had coef./s.d. ratios greater than

1.0, a further significant reduction in variance was

obtained. Equations 2A and 2B, calculated for the "odds" and "evens" in the array of cements

5 A tabulation of the "F" values for reduction in variance for all equations compared is presented in table 13-57. Presented also are the critical values for "F" which must be equaled or exceeded for significance at the

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

indicated that C3A, NaaO, MgO, and Mn had

coef./s.d. ratios less than 1.0 in one or the other

of the smaller groups of cements.^

The major oxides CaO, SiOa, AI2O3, and Fe203 were used in eq 3 instead of the calculated potential compounds as in eqs 1 and 2. There was a

significant reduction in variance, and when the

trace elements Mn, Rb, and Zr were used with the

commonly determined variables in eq 4 there was

a further reduction in variance. (See table 13-57.)

In eqs 4A and 4B calculated for the "odds" and

* As has been indicated in previous sections of this series of articles, this may occur if a number of cements having higher than normal values for an independent variable are included in one of the two groups. If the

coefficients of a variable in smaller groups, i.e. the odds and evens, both

are significant, a greater confidence can be placed on the significance of the variable of the equation where all cements were included.

elasticity in 10^ psi after H days moist curing of Series O concretes made of AE +

independent variables

AI2O3 FejOj S03 NajO KjO MgO

+0.146 +0.302 +0.240 +0.0138

(0.042) (0.083) (0.071) (0.0123) +0.160 +0.260 +0.148 +0.0240

(0.041) (0.082) (0.078) (0.0125) +0.237 +0.272 +0.124 * +0.0130

(0.057) (0.105) (0.110) (0.0180) +0.079 * +0.116 +0.205 +0.0369

(0.062) (0.157) (0.121) (0.0178) +0.117 +0.315 +0.253 +0.0298

(0.067) (0.085) (0.073) (0.0257) +0.135 +0.273 +0.166 +0.0422

(0.057) (0.084) (0.081) (0.0257) +0.215 +0.284 +0.150 * +0.0296

(0.085) (0.108) (0.120) (0.0354)

* +0.070 * +0.140 +0.217 +0.0673

(0.085) (0.160) (0.122) (0.0402)

Mn Rb Zr S.D.

-0.0875 -0.0867

(0.0319) (0.0299) -0.0855 -0.0799

(0.0317) (0.0296) -0.1022 -0.0856

(0.0433) (0.0440) -0.0562 -0.0618

(0.0508) (0.0434)

-1.188

(0.115) * -0.052

(0.154) -0.445

(0.181)

-0.176

(0.116) -0.042

(0.156) -0.416

(0.185)

+18.63

(7.76) +14.92

(9.92) +19.82

(12.90)

+18.39

(7.77) +14.57

(9.97) +19.91

(12.93)

+0.561

(0.331) +1.675

(0.853) +0.488

(0.383)

+0.617

(0.339) +1.795

(0.881) +0.555

(0.392)

0.1763

0.1718

0.1678

0.1762

0.1765

0.1720

0.1684

0.1765

of elasticity in 10^ psi after H days moist curing of Series 0 concretes made of NAE

independent variables

SO3 NazO K20 MgO Mn Rb Zr

-0.112 -0.101

(0.025) (0.021) -0.092 -0.077

(0.033) (0.030) * -0.035 * +0.007

(0.050) (0.055) -0.108 -0.108

(0.048) (0.039)

+0.165

(0.042) +0.177

(0.041) +0.178

(0.060) +0.203

(0.063) +0.097

(0.048) +0.141

(0.058) +0.236

(0.090) +0.141

(0.083)

+0.300

(0.084) +0.257

(0.085) +0.212

(0.109) +0.335

(0.148) +0.295

(0.085) +0.266

(0.087) +0.276

(0.113) +0.333

(0.149)

+0.252

(0.071) +0.152

(0.081)

* +0.112

(0.125) +0.119

(0.115) +0.236

(0.076) +0.166

(0.085) +0.191

(0.131) +0.118

(0.117)

+0.0204

(0.0126)

* +0.0132

(0.0180) +0.0274

(0.0186)

+0.0326

(0.0266) +0.0835

(0.0439)

* +0.0228

(0.0362)

-0.183

(0.119) -0.415

(0.164) +0.193

(0.191)

+15.39

(7.91) +25.07

(11.53) *+3.98

(12.11)

+0.580

(0.332)

* +0.586

(2.245) +0.526

(0.362)

-0.179

(0.121) -0.401

(0.162)

* +0.187

(0.200)

+15.26

(7.92) +25.10

(11.37) *+3.85

(12.21)

+0.619

(0.340) -0.380

(2.281) +0.511

(0.381)

73
"evens" in the array of cements, the variables

SO3, Na20, MgO, and Mn had coef./s.d. ratios

less than 1.0 in one or the other of the equations

for the smaller groups of cements.

A similar series of equations is presented in table 13-3 for the Series 0 concretes made with

NAE cements. The coefficients for the air content were highly significant even with the concretes made with non-air-entraining cements. The coefficients of the other variables, the coef./s.d. ratios,

and S.D. values were in reasonable agreement

with those of table 13-2 where the air-entraining

cements were included. Including the trace ele- ments in eqs 2 and 4 together with- commonly determined variables resulted in a reduction of variance

significant at the a = 0.05 level. In eqs 2A, 2B,

4A, and 4B calculated for the "odds" and "evens"

the coef./s.d. ratio of C4AF, AI2O3, FesOa, K2O,

MgO, Mn, Rb, and Zr was less than 1.0 in one or the other of the equations for the smaller groups

of cements.

Using the independent variables of eq 2, table

13-3, and the ranges of these variables, values were calculated for their contributions and ranges

of contributions to the dynamic modulus after 14

days moist curing. These calculated values, as presented in table 13-4, are approximations based on a single equation, and somewhat different

Table 13-4. Calculated contributions of independent variables

to ODH, the 1 It-day dynamic modulus of Series O concretes

Inde- pendent

variable

Range of variables

(percent)

Coefficients from eq 2

table 13-3

Calculated

contributions

to OD14

Calculated range of contributions to 0D14

Const. = +3.62

Air-content, NAE

cements- 0 to 4.5 -0.1346 0 to -0.61 0.61 C3A* 1 to 15 +0.01056 +0.01 to +0.15 0.14 C3S 20 to 65 +0.0197 +0.39 to +1.28 0.89 CiAF* 1 to 16 -0.0144 -0.01 to -0.23 0.22 SO3 1.2 to 3.0 +0.177 +0.21 to +0.53 0.32 NajQ 0 to 0.7 +0.257 0 to +0.17 0.17 K2O* 0 to 1.1 +0.152 0 to +0.17 0.17 MgO* 0 to 5 +0.0204 0 to +0.10 0.10 Mn* 0 to 1.0 -0.183 0 to -0.18 0.18 Rb* 0 to 0.01 +15.39 0 to +0.15 0.15 Zr* 0 to 0.5 +0.580 0 to +0.29 0.29

values would be obtained by the use of other

equations.^ Increases in air content were associated with

decreases in the dynamic modulus values. In- creases of C3S, SO3, and Na20 were associated

with increases of dynamic modulus. Differences

in the air content and C3S had the greatest calculated contribution to the 14-day dynamic modulus

as determined from this equation.

6.1.2. Dynamic Modulus of Series A Concretes The frequency distribution of the dynamic

modulus of the Series A concretes is presented in

table 13-5. There was a broad distribution of

values and an overlapping of the values for the

different types of cement. The majority of the

concretes made of the air-entraining cements, as with the Series 0 concretes (table 13-1), had lower

values for dynamic modulus than the over-all

average.

A series of equations is presented in table 13-6

to indicate the relationship of various independent

variables to the dynamic modulus of Series A

concretes made of AE + NAE cements. The use

of the air content as an independent variable in

eq 1, or w/c in eq 2 or both in eq 3 resulted in a

significant reduction in variance. (See table 13-57).

The additional use of the commonly determined

variables C3S, C4AF, SO3, Na20, K2O, and MgO

in eq 4 resulted in a highly significant reduction

in variance. The coefficient for w/c was greater in

magnitude and had a higher coef./s.d. ratio in

eq 4 than in eq 3. It was indicated in a previous

section [16] that a number of independent variables was related to the water requirement of the

cements, and it may be that the differences in

these coefficients indicate some interaction between water/cement ratio and other independent

variables.

With the use of the commonly determined

variables together with the trace elements Rb

and Mn in eq 5 there was a reduction in variance

*Coef[icient of doubtful significance as coef./s.d. ratio was less than 2.

' Computations for contributions to dynamic modulus at other ages have been made from similar equations, i.e., one selected from the NAE

cements containing one or more of the potential major compounds, other commonly determined variables, and trace elements in order that the trends may be followed more easily. Table 13-5. Frequency distribution of cements with respect to ADll^, the dynamic modulus of elasticity of Series A concretes

after H days moist curing

Dynamic modulus of elasticity, psi X 10 —6

3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 Type cement to to to to to to to to to to to Total

3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

Number of cements

I 3

3

4

6 20 32 14 1 2 1 79

867

320

315

lA 1 4

II 2 8

1 2111

23 8 1 HA 1 III 5

1

1

11 2 1 IIIA 2 IV, V 1 1 1 2 6 2 1 Total 2 2 7 12 23 45 62 34 4 3 1 195

74
significant at the a = 0.05 level. (See table 13-57.)

The coef./s.d. ratios of Na^O, Rb, and Mn were

less than 1.0 in eqs 5A or 5B calculated for the

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

The use of the major oxides in eq 6 together

with other commonly determined variables re- sulted in an S.D. value not significantly different

from that of eq 4 where the potential compounds

were used as independent variables. The additional use of the independent variables MgO, Rb,

and Mn in eq 7 did not result in a reduction of variance significant at the a = 0.05 level. The eqs

7A and 7B calculated for the "odds" and "evens"

in the array of cements indicated that CaO, SO3,

Na20, K2O, MgO, and Rb had coef./s.d. ratios of

less than 1.0 in one or the other or both of the

equations for the smaller group of cements.

An analogous series of equations calculated for the dynamic modulus after 14 days moist curing

of Series A concretes made with NAE cements

is presented in table 13-7. As indicated in eqs 1, 2, and 3, the coefficients for air content and w/c

were not significant. In eqs 4 through 7 the coefficients for air content and w/c were highly significant when used together with other independent variables. Increases in both air content and

w/c were associated with decrease in the dynamic

modulus. The use of the commonly determined

variables in eqs 4 and 6 resulted in a highly significant reduction in variance. The additional use

of the trace elements Rb, Mn, and Cu in eqs 5

and 7 resulted in a reduction in variance significant at the 5.0-percent level in eq 7 but not in eq 5. (See table 13-57.)

In equations calculated for the "odds" and

"evens" in the array of cement (eqs 5A, 5B, 7A,

and 7B) there were instances where the coef./s.d.

ratios of SO3, NaaO, K2O, MgO, Rb, Mn, and Cu

were less than 1.0 in one or the other or both of the equations for the smaller groups of cement.

Using the independent variables of eq 5 table

13-7 and the ranges of these variables, values were calculated for their contributions and ranges

of contributions to the dynamic modulus after 14

days moist curing. These calculated values are presented in table 13-8. Increases of air content,

w/c, C4AF and Mn were associated with decreases

of the dynamic modulus values. Increases of C3S,

SO3, Na20, K2O were associated with increases of the dynamic modulus. Of these variables, differ- ences of air content, w/c, and C3S showed the

greatest calculated contribution.

6.2. Dynamic Modulus After 28 Days Drying

6.2.1. Dynamic Modulus of Series O Concretes

The frequency distribution of the dynamic

modulus after 28 days drying for the Series 0

concretes is presented in table 13-9. The concrete specimens were moist cured for 14 days and then

dried in laboratory air for 28 days. There was a broad distribution of results and an overlapping

of the values for the concretes made of the differ- ent types of cement.

Variables associated with the dynamic modulus

after 28 days drying of the Series 0 concrete made

of AE + NAE cements are presented in table

13-10. The use of the independent variables, air content, C3A, C3S, C4AF, SO3, Na20, APF, and

MgO in eq 1 resulted in a highly significant re- duction in variance. (See table 13-57.) As indicated in eq 2, Cu was the only trace element

having a coef./s.d. ratio greater than 1.0 when

used as an independent variable together with

commonly determined variables. The reduction

in variance was not significant at the 5.0-percent

level. Equations 2A and 2B indicate that C3A, fine- ness, and Cu had coef./s.d. ratios of less than 1.0

in one of the equations for the smaller groups of cements.

The use of Si02, AI2O3, and Fe203 together with

other commonly determined variables in eq 3

resulted in a significant reduction in variance

(See table 13-57) but the additional use of Cu in eq 4 did not result in a reduction of variance significant at the 5.0-percent level. In equations for the "odds" and "evens," 4A and 4B, the coef./s.d.

ratios of Na20 and Cu were less than 1.0 in one

or the other of the equations for the smaller

groups of cement.

A similar series of equations for the NAE

cements is presented in table 13-11. The coeffi- cients of the independent variables, the coef./s.d.

ratios, and the S.D. values obtained were in

reasonable agreement with the preceding table

where the AE cements were included.

Using the independent variables of eq 2, table

13-11, and the ranges of these variables, calculations were made of the estimated contributions

and ranges of contributions to the dynamic modulus after 28 days drying for the Series 0 concretes. These calculated values are presented in table 13-12. It may be noted that an increase in C3S and probably NaoO was associated with an

increase in dynamic modulus. Increases in air content, SO3 and probably C4AF and fineness were associated with a decrease in dynamic modulus. Of these independent variables, differences

in air content, C3S, and SO3 showed the greatest

calculated ranges of contribution to OD42.

6.2.2. Dynamic Modulus of Series A Concretes The frequency distribution of the dynamic modulus after 28 days drying of the Series A concretes

is presented in table 13-13. There was a broad

distribution of values and an overlapping of the

values obtained with the different types of cement.

The concrete specimens were moist cured 14 days

and then dried in laboratory air for 28 days.

Selected equations are presented in table 13-14

to indicate the independent variables associated

with the dynamic modulus values. Equation 1 indicates the effect of air content, eq 2 the effect of the w/c, and eq 3 the effect of both of these vari75
Table 13-6. Coefficients for equations relating ADlIf, the dynamic Young's modulus

NAE cements, to various

Eq. No. Note 10« psi Const.

1 1 AD14 +4.893

s.d. = (0.027)

2 1 AD14 +2.498

s.d. = (0.551)

1 AD14 +5.928

s.d. = (0.798)

4 1 AD14 +8.044

s.d. = (0.615)

1 AD14 = +7.870

s.d. (0.611) 5A 2 AD14 (odd) +9.259

s.d. = (0.962) 5B 3 AD14 (even)

s.d. +6.838 = (0.781) 6 1 AD14 +9.244

s.d. = (1.336)

7 1 AD14 +7.445

s.d. (2.530) 7A 2 AD14 (odd)

s.d. +13.057

(4.015) 7B 3 AD14 (even)

s.d. +7.744

(3.583)

Air content w/c C3S C4AF

-0.0648

(0.0092)

-0.0786

(0.0141) -0.1451

(0.0111) -0.1406

(0.0111) -0.1600

(0.0157) -0.1248

(0.0162) -0.1466

(0.0116) -0.1427

(0.0116) -0.1654

(0.0164) -0.1259

(0.0170)

+3.551

(0.864) -1.580

(1.218) -6.703

(0.931) -6.435

(0.927) -8.114

(1.486) -5.275

(1.147) -6.932

(1.007) -6.689

(0.999) -8.823

(1.600) -5.350

(1.234)

+0.0189

(0.0021) +0.0190

(0.0021) +0.0190

(0.0029) +0.0212

(0.0030)

-0.0291

(0.0064) -0.0273

(0.0064) -0.0453

(0.0096) -0.0109

(0.0084)

Note 1, 173 cements, Avg. Note 2, 87 cements Nore 3, 86 cements

4.762 X 106 p3i, S.D. = 0.2860 X 10^ psi. *Coef./s.d. ratio less than 1.

Table 13-7. Coefficients for equations relating ADll^, the dynamic Young's modulus

cements, to various

Note 10' psi

AD14

s.d. AD14

s.d. AD14

s.d. AD14

s.d. AD14

s.d. AD14 (odd)

s.d. AD14 (even)

s.d. AD14

s.d. AD14

s.d. AD14 (odd)

s.d. AD14 (even)

3.d.

Const.

: +4.786

(0.0392)

: +5.218

(0.657) +5.196

(0.817) +7.930

(0.659) +7.784

(0 652)

: +8.409

(0.964) +7.375

(0.828) +9.385

(1.375) +9.991

(1.396)

: +8.560

(2.003) +13.090

(2.030)

Air content

1^+0.0087

(0.0221)

*+0 0012

(0 0266) -0 1196

(0 0213) -0 1149

(0 0215) -0 0889

(0 0332) -0 1492

(0 0260) -0 1222

(0 0216) -0 1173

(0 0217) -0 0877

(0 0331) -0 1416

(0 0273)

w/c

* -0.654

(1.024) * -0.622

(1.236) -6.619

(0.999) -6.345

(0.990) -6.821

(1.449) -6.169

(1.278) -6.987

(1.077) -6.750

(1.604) -7.243

(1.516) -6.034

(1.419)

CsS

+0.0189

(0.0022) +0.0186

(0.0022) +0.0160

(0.0031) +0.0229

(0.0030)

C4AF

-0.0280

(0.0066) -0.0240

(0.0069) -0.0358

(0.0105) -0.0134

(0.0087)

CaO

+0.0638

(0.0140) +0.0545

(0.0145) +0.0667

(0.0214) +0.0318

(0.0195)

Note 1, 162 cemente, S.D. = 0.2466 x lO^ psi Note 2, 81 cements

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

76
of elasticity in 10^ psi after lU days moist curing of Series A concretes made of AE +

independent variables

AI2O3 FezOa SOa NaaO KjO MgO Rb Mn S.D.

0.2529

0.2736

0.2524

+0.208

(0.043) +0.211

(0.042) +0.114

(0.066) +0.255

(0.054) +0.134

(0.049) +0.161

(0.058)

* -0.011

(0.097) +0.181

(0.073)

+0.290

(0.080) +0.270

(0.079)

* +0.061

(0.131) +0.271

(0.100) +0.273

(0.081) +0.266

(0.083)

* -0.018

(0.144) +0.262

(0.107)

+0.303

(0.066) +0.222

(0.073) +0.455

(0.111)

* -0.001

(0.099) +0.289

(0.074) +0.210

(0.081) +0.394

(0.121) * -0.018

(0.117)

+0.0159

(0.0121) +0.0226

(0.0123) +0.0244

(0.0177) +0.0320

(0.0166)

0.1698

+14.86

(7.68)

* +5.86

(11.93) +21.34

(9.65)

-0.185

(0.111) * -0.116

(0.139) -0.282

(0.197)

0.1675

0.1722

0.1518

-0.153

(0.022) -0.139

(0.028) -0.173

(0.042) -0.170

(0.041)

-0.126

(0.025) -0.111

(0.032) -0.125

(0.048) -0.148

(0.044)

-0.126

(0.021) -0.105

(0.030) -0.201

(0.049) -0.070

(0.038)

0.1706

+0.0277

(0.0249)

* -0.0054

(0.0396)

* +0.0252

(0.0327)

+14.16

(7.78) *+1.42

(12.48) +21.71

(9.86)

-0.193

(0.114) -0.152

(0.143) -0.307

(0.218)

0.1683

0.1721

0.1538

of elasticity in 10^ psi after H days moist curing of Series A concretes made of NAE

independent variables

SOa NajO K2O MgO Rb Mn Cu

-0.123 -0.125

(0.026) (0.022) -0.125 -0.118

(0.026) (0.022) -0.083 -0.127

(0.035) (0.035) -0.207 -0.120

(0.039) (0.028)

+0.225

(0.045) +0.227

(0.044) +0.260

(0.065) +0.187

(0.057) +0.148

(0.050) +0.140

(0.050) +0.201

(0.077)

* +0.034

(0.069)

+0.269

(0.082) +0.248

(0.082)

* +0.107

(0.134) +0.316

(0.095) +0.248

(0.084) +0.218

(0.084)

* +0.089

(0.138) +0.272

(0.101)

+0.273

(0.069) +0.173

(0.078) +0.124

(0.121)

* +0.037

(0.100) +0.245

(0.078) +0.135

(0.086)

* +0.085

(0.130)

* +0.019

(0.115)

+0.0151

(0.0124) +0.0207

(0.0126) "+0.0059

(0.0185) +0.0652

(0.0172)

+12.59

(7.83) *+6.67

(11.33) +29.53

(10.32)

-0.239

(0.118) -0.380

(0.157)

* -0.067

(0.167)

-2.11

(1.66) -6.56

(2.54)

* +0.64

(2.02)

+11.41

(7.90) *+3.93

(11.62) +27.55

(10.64)

-0.267

(0.121) -0.420

(0.160)

* -0.161

(0.184)

-2.14

(1.66) -6.30

(2.55) *-0.01

(2.09)

77
Table 13-8. Calculated contributions of independent variables

to ADH, the H-day dynamic modulus of Series A concretes

Calculated Inde- Range of Coefficients Calculated range of pendent variables from eq 5 contributions contribuvariable (percent) table 13-7 to AD14 tions to AD14

Air- Const. = +7.78

content, NAE

cements. 0 to 4.5 -0.1149 0 to -0.52 0.52 w/c 0.6 to 0.7 -6.345 -3.81 to -4.44 0.63 C3S 20 to 65 +0.0186 +0.37 to +1.20 0.83 CiAF 1 to 16 -0.0240 -0.02 to -0.38 0.36 SO3 1.2 to 3.0 +0.227 +0.27 to +0.68 0.41 NasO 0 to 0.7 +0.248 0 to +0.17 0.17 K2O 0 to 1.1 +0.173 0 to +0.19 0.19 MgO* 0 to 5 +0.0207 0 to +0.10 0.10 Rb* 0 to 0.01 +12.59 0 to +0.13 0.13 Mn 0 to 1.0 -0.239 0 to -0.24 0.24 Cu* 0 to 0.05 -0.211 0 to -0.01 0.01

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

ables. The sign of the coefficient for w/c was

positive in eq 2 and negative in eq 3 and not

highly significant. In eq 4, where other commonly

determined variables were included, the coeffi- cients for both air content and w/c were negative

and highly significant. The use of the independent

variables in eqs 1, 2, or 3 resulted in a significant

reduction in the S.D. value. (See table 13-57.)

With the additional use of the trace elements Cu,

Li, and Zr in eq 4, the reduction in variance was

significant at the 5.0-percent level. Equations 5A and 5B calculated for the "odds"

and "evens" in the array of cements indicated

that C3A, C4AF, fineness. Loss, Cu, Li, and Zr

had coef./s.d. valyes less than 1.0 in one or both

of the equations calculated for the smaller groups

of cement.

The use of Si02, AI2O3, and Fe203 in eq 6 instead

of the potential compounds but with other com- monly determined variables resulted in an S.D.

value similar to that of eq 4. The variables Loss

and Zr had coef./s.d. ratios less than 1.0 in eq 6. The use of the trace elements Cu and Li in addition to the commonly determined variables re- sulted in a reduction in variance significant at the

5.0-percent level. (See table 13-57.)

Equations calculated for the dynamic modulus

after 28 days drying of the Series A concretes made

with the NAE cements are presented in table

13-15. In eqs 1, 2, and 3 the air content and w/c

were not significant when used as independent

variables. However, in eqs 4 through 7, where

other commonly determined variables were in- cluded, the coefficients were highly significant for both air content and w/c. The use of the com- monly determined variables in eq 4 resulted in a

highly significant reduction in variance, but with

the added trace elements Cu, Li, and Zr in eq 6

the reduction in variance was significant at the

5.0-percent level. (See table 13-57.)

Calculations made for the "odds" and "evens"

in the array of cements are presented in eqs 5A

and 5B. There were instances where the independent variables MgO, fineness. Loss, Cu, Li,

and Zr had coef./s.d. ratios of less than 1.0 in one

or the other of the equations for the smaller

groups of cement.

With the use of SiOj, AI2O3, and Fe203 instead

of the potential compounds but with the other

commonly determined variables, there was a

highly significant reduction in variance. The in- dependent variables. Loss and Zr, had coef./s.d.

ratios less than 1.0. The use of Cu and Li together

with commonly determined variables in eq 7

resulted in a reduction in variance significant at the 5.0-percent level. Equations calculated for the "odds" and "evens"

in the array of cements indicated that MgO, Cu,

and Li had coef./s.d. values of less than 1.0 in one or the other of the smaller groups of cement.

Using the independent variables of eq 5, table

13-15, and the ranges of these variables, calculations were made of the estimated contributions

to the dynamic-modulus values. These calculated

values together with the calculated ranges of

values are presented in table 13 16. Increase in C3S, SO3 and possibly MgO was associated with

higher dynamic-modulus values. Increases in air content, w/c and possibly C4AF, fineness, and Cu

were associated with decreases in the dynamicmodulus values. Differences in air content, w/c,

C3S, and SO3 showed the greatest calculated range

of contributions to AD42.

Table 13-9. Frequency distribution of cements with respect to 0D^2, the dynamic modulus of elasticity of Series 0 concretes

at i2 days after 1 k days moist curing and the storage in air for 28 days

Dynamic modulus of elasticity, 10» psi

Type cement

3.2 to

3.4

3.4

to

3.6

3.6

to

3.8

3.8 to

4.0

4.0

to

4.2

4.2 to

4.4

4.4 to

4.6

4.6 to

4.8

4.8 to

5.0

5.0 to

5.2

5.2 to

5.4 Total

Number of cements

I 2 7 13 33 20 6 1 82 lA 2 1 2 2 1 8

II 1 1 5 12 18 14 13 4 68 IIA.. 1 1 1 3

III 1 6 5 5 3 20 IIIA 2 1 3 IV, V 1 1 2 3 6 2 15

Total 2 4 3 3 13 22 39 54 40 15 4 199

78
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79
Table 13-12. Calculated contributions of independent vari- ables to 0Dl2, the dynamic modulus after lU days moist curing followed by 28 days in laboratory air of Series 0

concretes.

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 2 contributions contribuvariable (percent) table 13-11 to OD42 tions to OD42

Const. = +3.61

Aircontent, NAE

0 to 4.5 Q J525 u to —u.oy 0 69 CiA** 1 to 15 -o!oio -0.01 to -0.15 o!i4 CsS 20 to 65 4-0.0178 +0.35 to +1.16 0.81 CiAF 1 to 16 -0.0206 -0.02 to -0.32 0.30 SO3 1.2 to 3.0 -0.534 -0.64 to -1.60 0.96 NasO 0 to 0.7 +0.214 0 to +0.15 0.15 APF *2500 to 5500 -0.000115 -0.29 to -0.63 0.34 MgO** 0 to 5.0 +0.0228 0 to +0.11 0.11 Cu** 0 to 0.05 -3.195 0 to -0.16 0.16

*cmVg.

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

6.3. Dynamic Modulus After 56 Days Drying

6.3.1. Dynamic Modulus of Series O Concretes The frequency distribution of the dynamic

modulus of Series 0 concretes after 56 days drying

is presented in table 13-17. The concrete speci- mens had been moist-cured for 14 days then dried

in laboratory air for 8 weeks. There was a broad

distribution of values and an overlapping of values

obtained with the different types of cements.

Equations are presented in table 13-18 indicating the variables associated with the dynamic

modulus of the air-dried Series 0 concretes made

with AE + NAE cements. Commonly determined

variables having a coef./s.d. ratio greater than 1.0 when used in the multivariable equation (eq 1)

resulted in a highly significant reduction in vari- ance. (See table 13-57.) The only trace element

Table 13-13. Frequency distribution of cements with respect to ADl^2, the dynamic modulus of elasticity of Series A concretes

at lt2 days {moist curing IJ^ days and then drying in laboratory air for 28 days)

Dynamic modulus of elasticity, 10* psi

3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 Type cement to to to to to to to to to to to Total

3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6

Number of cements

I 1

12

12

6

9

1 13

23

3

132

2

12

29 12 1 3 79

867

320

3

16

lA 1 II 16 12 5 IIA 1 III 2

2

5 6 1 IIIA

IV, v 2 2 5 2

Total 2 2 4 11 28 46 55 31 12 3 1 195

Table 13-14. Coefficients for equations relating ADlt2, the dynamic Young's modulus

ratory air of Series A concretes made of AE +

Eq. No. Note 106 psi Const.

AD42

s.d. = +4.675 = (0.030) AD42

s.d. = +2.911 = (0.592) AD42

s.d. = +5.644 = (0.892) AD42

s.d. = +7.961 = (0.721) AD42

s.d. = +7.766 = (0.715) AD42 (odd)

s.d. = +9.511 = (1.166) AD42 (even)

s.d. = +5.855 = (0.957) AD42

s.d. = +15.23 = (1.15) AD42

s.d. = +14.89 = (1.14) AD42 (odd)

s.d. = +16.29 = (1.69) AD42 (even)

s.d. = +13.89 = (1.61)

Air content w/c CaA CaS CiAF SiOj

4..,

5-.

5A.

5B.

-0.0499

(0.0103)

7...

7A.

7B.

-0.0631

(0.0158) -0.1281

(0.0132) -0.1260

(0.0130) -0.1480

(0.0190) -0.0993

(0.0198) -0.1289

(0.0129) -0.1264

(0.0128) -0.1498

(0.0185) -0.1009

(0.0196)

+2.609

(0.928) -1.511

(1.360) -6.879

(1.134) -6.649

(1.121) -8.753

(1.868) -4.415

(1.456) -6.780

(1.114) -6.523

(1.102) -8.768

(1.821) -4.212

(1.432)

-0.0118

(0.0067) -0.0102

(0.0068)

* -0.0088

(0.0104) -0.0113

(0.0098)

+0.0174

(0.0026) +0.0173

(0.0026) +0.0149

(0.0037) +0.0211

(0.0037)

-0.0247

(0.0084) -0.0193

(0.0085) -0.0340

(0.0127)

* -0.0075

(0.0130) -0.212

(0.028) -0.207

(0.028) -0.197

(0.040) -0.232

(0.041)

Note 1, 173 cements, Avg. = 4.574 X 10« psi, S.D. = 0.2999 X 10' psi Note 2, 87 cements Note 3, 86 cements

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

80
having a coef./s.d. ratio greater than 1.0 when

used with other commonly determined variables was vanadium. The additional use of V in eq 2

did not result in a significant reduction in variance.

Equations 2A and 2B calculated for the "odds"

and "evens" in the array of cements indicated

that K2O as well as V had coef./s.d. ratios less than 1.0 in one or both of the smaller groups of cement.

Equations 3 and 4, calculated using the major

oxides instead of the potential compounds, re- sulted in approximately the same S.D. values.

The coef./s.d. ratio for K2O was less than 1.0, and

that for Loss in eq 4B was less than 1.0. The

average value for the dynamic modulus after 8

weeks drying was 4.43 X 10^ psi, after 4 weeks

drying it was 4.57 X 10" psi, and after 14 days

moist curing before the drying cycle, the average

value was 4.75 X 10" psi. (See tables 13-18, 13-10,

and 13-2.)

A similar set of equations for the Series 0 concretes made with NAE cements is presented in table 13-19. The use of the commonly determined

variables, air content, C3A, C3S, C4AF, SO3, K2O,

fineness, Loss, and MgO in eq 1 resulted in a

highly significant reduction in variance. The use

of V in eqs 2 or 4 in addition to other commonly

determined variables did not result in a reduction

in variance significant at the 0.05 probability level. The coefficient for the air content of the NAE

cements was highly significant, but the coef./s.d.

ratio was somewhat smaller than when the AE

cements were included as in the previous table. Using the coefficients of the independent variables of eq 2 of table 13-19 as well as their ranges

of values, calculations were made of their esti- mated contribution to the dynamic modulus after

56 days drying and the calculated ranges of these

contributions. These calculated values are pre- sented in table 13-20. Increases of C3S, SO,-, and

possibly loss on ignition and MgO were associated

with increases in dynamic modulus values. Higher

values for air content, CdA, C4AF, and fineness were associated with lower values for dynamic

modulus.

6.3.2. Dynamic Modulus of Series A Concretes

The frequency distribution of the dynamic

modulus of the air-dried Series A concretes is pre- sented in table 13-21. The use of a 5 ± 1-in slump

rather than a constant water/cement ratio re- sulted in slightly higher values for the AE cements

(types lA, IIA, and IIIA) than was observed in

table 13-17. There was a broad distribution of values and an overlapping of the values obtained

with the different types of cement.

Equations are presented in table 13-22 indicating the variables associated with the dynamic

modulus of the Series A concretes made of AE -f NAE cements. Equations 1, 2, 3, and 4 show that

using the air content and the water/cement ratio,

singly or together, and with other commonly determined variables, resulted in differences in the

values for the coefficients as well as in their coef./

s.d. ratios. Whereas the coefficient for w/c was

positive in eq 2, it was negative in eqs 4 through 7. As indicated in table 13-57, the reduction in vari0/ elasticity in 10^ psi after lU days moist curing followed by 28 days drying in labo- NAE cements, to variotis independent variables

AhOj FejOj SO3 MgO APF Loss Cu Li Zr S.D.

0.2821

0.2940

0.2819

-0.234 -0.152

(0.033) (0.022) -0.227 -0.136

(0.033) (0.023) -0.215 -0.173

(0.048) (0.035) -0.257 -0.111

(0.047) (0.032)

+0.517

(0.056) +0.508

(0.056) +0.503

(0.086) +0.439

(0.081) +0.379

(0.057) +0.365

(0.056) +0.388

(0.082) +0.283

(0.082)

+0.0421

(0.0133) +0.0348

(0.0138) +0.0350

(0.0203) +0.0429

(0.0197) -0.0277

(0.0143) -0.0352

(0.0144) -0.0334

(0.0202) -0.0322

(0.0203)

-0.000120

(0.000038) -0.000104

(0.000038) -0.000145

(0.000054)

* -0.000020

(0.000062) -0.000119

(0.000037) -0.000109

(0.000036) -0.000148

(0.000051)

* -0.000037

(0.000057)

+0.0629

(0.0314) +0.0452

(0.0319) +0.0751

(0.0491)

* -0.0180

(0.0465)

-4.41

(1.89) -5.33

(2.83) *-2.95

(2.99)

+9.11

(4.64) *+6.92

(7.53) *+6.33

(6.78)

+0.381

(0.372)

* +0.313

(0.424)

* +0.115

(0.982)

0.1944

0.1914

0.1984

0.1834

-4.33

(1.86) -5.81

(2.73) *-2.85

(2.96)

+8.34

(4.50) *+7.05

(7.12) *+5.85

(6.65)

0.1913

0.1885

0.1935

0.1817

81
Table 13-15. Coefficients for equations relating ADlt2, the dynamic Young's modulus of ratory air of Series A concretes made of NAE

Eq. No. Note 10^ psi Const.Air content w/c CaA CsS C4AF SiOj

1...

2

2

1

1

2

2

AD42 = +4.621

s.d. = (0.044) AD42 = +4.742

s.d. = (0.741) AD42 = +5.212

s.d. = (0.919) AD42 = +7.983

3.d. = (0.766) AD42 = +7.756

s.d. = (0.756) AD42 (odd) = +8.503

s.d. = (1.080) AD42 (even) = +6.899

s.d. = (1.084) AD42 = +15.07

s.d. = (1.19) AD42 = +14.71

s.d. = (1.18) AD42 (odd) = +15.17

s.d. = (1.63) AD42 (even) =+14.33

s.d. = (1.79)

* -0.0153

(0.0249)

2

* -0.226

(1.155)

* -0.895

(1.391) -6.905

(1.202) -6.645

(1.186) -7.462

(1.703) -5.382

(1.688) -6.898

(1.186) -6.624

(1.173) -7.542

(1.662) -5.286

(1.660)

3

* -0.0260

(0.0300) -0.1270

(0.0239) -0.1231

(0.0240) -0.1195

(0.0371) -0.1378

(0.0330) -0.1323

(0.0235) -0.1286

(0.0236) -0.1263

(0.0359) -0.0388

(0.0323)

4 -0.0127

(0.0068) -0.0111

(0.0069) —0.0164

(0.0116) —0.0144

(0.0089)

+0.0172

(0.0026) +0.0170

(0.0026) +0.0152

(0.0038) +0.0183

(0.0039)

-0.0263

(0.0084) -0.0206

(0.0085) —0.0408

(0.0145) —0.0129

(0.0110)

5

5A

5B

6 -0.205

(0.029) -0.199

(0.028) -0.190

(0.040) -0.214

(0.044)

7

7A

73.

Note 1, 162 cements, Avg. = 4.598 X 10^ psi, S.D. = 0.2777 X 10^ psi Note 2, 81 cements

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

Table 13-16. Calculated contributions of independent vari- ables to AD1^2, the dynamic modulus after H days moist curing followed by 28 days in laboratory air of Series A

concretes

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 5 contributions contribuvariable (percent) table 13-15 to AD42 tions to AD42

Const. = +7.756

Aircontent, NAE

cements. 0 to 4.5 -0.1231 0 to -0.55 0.55 w/c 0.6 to 0.7 -6.645 -3.99 to -4.65 0.66 CsA** 1 to 15 -0.0111 -0.01 to -0.16 0.15 CsS 20 to 65 +0.0170 +0.34 to +1.11 0.77 C4AP 1 to 17 -0.0206 -0.02 to -0.35 0.33 SO3 1.2 to 3.0 +0.513 +0.62 to +1.54 0.92 MgO 0 to 5.0 +0.0344 0 to +0.17 0.17 APF *2500 to 5500 -0.000093 -0.23 to -0.51 0.28 Loss**. 0.3 to 3.3 +0.0340 +0.01 to +0.11 0.10 Cu 0 to 0.05 -4.41 0 to -0.22 0.22 Li** 0 to 0.02 +9.20 0 to +0.18 0.18 Zr** 0 to 0.5 +0.468 0 to +0.23 0.23

*cmVg.

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

ance was highly significant for each of the first four equations. The use of Li (the only trace element with a coef./s.d. ratio greater than 1.0)

in eqs 5 and 7 together with the commonly determined variables did not result in a significant

reduction in variance.

In equations calculated for the "odds" and

"evens," eqs 5A, 5B, 7A, and 7B, there were

instances where the coef./s.d. ratios of K2O, fine- ness, and Li were less than 1.0 in one or both of the equations for the smaller groups of cements.

The coef./s.d. ratio for Loss was less than 1.0

when included in equations calculated using the

oxides (eqs 6 and 7) rather than the potential

compounds as in eqs 4 and 5. A similar series of equations is presented in table 13-23 for the NAE cements. Equations 2

and 3 of this table do not indicate a relationship

to the water/cement ratio. However, when w/c

was included with other commonly determined

variables as in eqs 4 and 6, its coefficient was

highly significant. The relationship of various

independent variables to the water requirements

of pastes, mortars, and concrete was discussed in

part 1, section 2 of this series of articles [16]. The

use of the commonly determined variables, air content, w/c, C3A, C3S, C4AF, SO3, K2O, APF,

Loss, and MgO in eq 4 resulted in a highly significant reduction of variance. (See table 13-57.)

The only trace element that had a coef./s.d. ratio

greater than 1.0 when used with the commonly

determined variables was Li. The use of Li in eqs

5 and 7 did not result in a reduction of variance

significant at the 5.0-percent level. There were instances in equations calculated

for the "odds" and "evens" (eqs 5A, 5B, 7A, and

7B) where the coef./s.d. ratios for fineness, MgO,

and Li were less than 1.0 in one or the other of the

pairs of equations calculated for the smaller groups

of cements.

Using the coefficients of the independent variables of eq 5 of table 13-23 as well as their ranges

of values, calculations were made of their esti- mated contributions to the dynamic modulus after

56 days drying and the calculated ranges of these

82
elasticity in 10^ psi after H days moist curing followed by 28 days drying in labo- cements, to various independent variables

i\I2v/3 SO3 MgO APF i., .JO S.D.

0.2783

0.2786

0.2788

+0.521

(0.056) +0.513

(0.056) +0.526

(0.088) +0.490

(0.081) +0.387

(0.057) +0.373

(0.057) +0.400

(0.087) +0.324

(0.083)

+0.0415

(0.0134) +0.0344

(0.0139)

* +0.0096

(0.0220) +0.0635

(0.0188) -0.0262

(0.0143) -0.0338

(0.0144) -0.0563

(0.0228)

* -0.0110

(0.0191)

-0.000110

(0.000039) -0.000093

(0.000038)

* -0.000061

(0.000066) -0.000114

(0.000048) -0.000109

(0.000037) -0.000100

(0.000037) -0.000063

(0.000061) -0.000120

(0.000046)

+0.0534

(0.0318) +0.0340

(0.0322)

-rU.uoyy

l,U.UDO^ )

0.1913

-4.41

(1.88) — / .0 ( V^.OD) *-1.35

(2.79)

+9.20

(4.62)

* +7.34

(7.78) +6.93

(6.72)

+0.468

(0.367)

* -4-2.514

+0.478

(0.357)

0.1877

0.1984

0.1737

-0.229

(0.033) -0.221

(0.033) -0.222

(0.043) -0.247

(0.053)

-0.153

(0.022) -0.137

(0.023) -0.183

(0.037) -0.111

(0.031)

0.1890

-4.27

(1.86) -8.07

(2.78) *-1.71

(2.74)

+8.39

(4.51) *+6.77

(7.06) +7.91

(6.63)

0.1860

0.1954

0.1717

Table 13-17. Frequency distribution of cements with respect to OD70, the dynamic modulus of elasticity of Series 0 concretes

at 70 days {lit days moist curing and then storage in laboratory air for 8 weeks)

Dynamic modulus of elasticity, 10» psi

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 Type cement to to to to to to to to to to to Total

3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4

Number of cements

I 2

1

6

1

9 15 31 10 12 3 82

868

320

315

lA 3

1

1

1 3

II 4 21

1

1

15 10 10 1 IIA

III 3

14

4 4 5 3 IIIA 1

1

1 IV, V 2 2 4 1 1

Total 6 3 3 12 16 42 64 25 27 9 3 199

contributions. These calculated values are pre- sented in table 33-24. Higher values for air content, w/c, C3A, and C4AF were associated with

lower values for dynamic modulus. Higher values

for C3S, SO3, and probably KoO, Loss, and MgO

were associated with higher values for dynamic

modulus of the air-dried concrete.

6.4. Dynamic Modulus After 28 Days Resoaking

6.4.1. Dynamic Modulus of Series O Concretes

After 14 days moist-air curing, then 8 weeks

drying in laboratory air, the concrete specimens

were placed in water and the dynamic modulus

was again determined after 28 days of soaking.

The frequency distribution of dynamic modulus

after 28 days resoaking of the Series 0 concretes

is presented in table 13-25.

There was a fairly broad distribution of values

for the concretes made of NAE cements and an

overlapping of the values for the cements of the

different types.

A series of equations is presented in table 13-26

to indicate the independent variables found to have coef./s.d. ratios greater than 1.0 and their

relation to the values for dynamic modulus after

28 days resoaking. The use of the commonly determined variables, air content, C3A, C3S, C4AF,

SO3, APF, and Loss in eq 1 resulteci in a highly

significant reduction in variance. (See table 13-57.)

The additional use of the trace elements Ba, Cu,

and Zr in eq 2 resulted in a further significant

reduction in variance. In equations calculated for the "odds" and "evens" in the array of cements

(eqs 2A and 2B) there were instances where APF,

Loss, Cu, and Zr had coef./s.d. ratios of less than

1.0 in one or the other of the equations for the

smaller groups of cements.

83
m

N

CO rH OO

o'd O 00

rH

q do

rHq 00

1-i

d

00 00 ON

qqdd+^

T-j

q

dd

oec

ooo qqdd+"•' N CO

1-H

q

d

d

t-o

00 03

05 -H o q dd

04Oq dd

qqd d

1-1

n

t- o q q d d

If c- ooo

qqd d

to -d" CO o

CO

qq dd

coo CON qqd d

iHU5 qqOO

qi CO

CO 00

COo o

rH

O «NNqqdd+^

00 to rHCO

rH

O

OO o q d d

00 t-

(N CO rH O Oo o o o

ONin

1-1 o o o OO

qqddI ^

in o o OO

OO

NU5

NCO

rH

O OO

qqddI ^

rHCOCO rHO OOO O qqddI '-'

OO

qqddI ~^

00OOo o q o ddI " V tc ot- r^q d d

N«0 O trH q d d

00 tN OS

to rH Ol N rH q q d d o o

=^5

N

CO o lO o d d

U5 U5

U3

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X TP Ol 00 cooo ooco •^q ii5q dd ddCO

N

N inO d d

«0 CO

CO »n dd

in

N t- 00

CO

q

dd

O rH ^_o dd

c- o * N rH OO

N in CO

r^

O

OrH

(O CO N q ddI ^ o o o to

inNqddI

CO-*

00N

q ddI "

in 00

rH

N

N

q

dd

CO 00 rHN N q d d

teos ON OS CO CO ^ rH q N q d d d d

N 00 oteo o qoddI ^

qodd

COCO OON rHO qo

dd

rH CO OON rHO q q dd

WrH NtO

t- COO CO rHO NO qo qq OO dd

*oCO to N O o o ddI ^

toco into N O o o

t-Tjl 0>0i NOo o

to

N OiOO rHO qqddI

rnq ddrHO dd

t-Ol ino

rnq ddI "

to 00

t- 1-

in o rH O

ojin laioo coo OOrH

•*rH t-rH rHO rHO OOI ^ OO

^t rH

COO

N Ol

in rH

COO CO o

fCO

to to OON

co'd coo OO

O

m 9-^ O oi

II II II II

OO

II II

OiH rHrH

^en) •o

0) o o o o o

t>O

m 0-6 O si

O oi

t-Q-o O M

O

m

1H rH

N CO rH rH

ii c c c

a; a; 0) .2 566 D i> QJ

e4

u o u

ooo 2ZZ e«

to

Sec

CO ^

s|

s> « ~ s

13

II= 1

CO § S S o

Si «

ta o <= s<

Eh

ON 1 CO rH q o dd I O 03 I US I • OO

m CO COOi ooo

rH

dI « rH t-eo N rH qqdd

oo+-'

CON

CO o

"5"*. d rH I o o

OO

in o

OON NN

rtC- f rH O O dd

qqdd

Nin 005

too) tOrH OOO q •* rH d d rH

mo

qqd dI

in rH COCO qqo'd +^

oo•H . . ... llrH CON qq qq d d d d I ^ I w N rH 00 t> CO CO t— ^ qq ©q dd dd +- -f^

NNlOO

rHN

qqd dI

o>te N T» qqddI

in c- NCO

rH

O OOo o OO

in 00 rHO OOo o qoddI

rH

O

OO

O

q o ddI ^

to 00

to in ooo o o o qqddI

OOOO

NtO

•*co

rH

O

OO OO

qqd dI -

00 o>

t- If

rH

O

Oq

q

dd

ot- o o ooo o qoddI I NO? I COC- oo

^o>

Ntrnq dd+^ oo

com

to rH O rH do"

OiCO

in in inq dd

in

q dd

rH NOl

in o d d

Ol 1-t in c—

in o dd

NCO

•^in

-9

q dd+^

in in rfq dd

O Oi CO CO NOO OCTf q o dd dd

Oi rH tfN

rH

q

do" I "

OOrH

•<f

N rHO ddI ^ f o> eorH toN ^eo rHO rHO dd dd

NNt-CO NOddItON

t-eo N o

in TJ« rH ^ N q CO q dd dd

too NNNqddI•*Oi NNNOAOO OtO

Oi ec CO ^ rHO NO dd do I I -

c-oo

00 t- N O o o

tOOi

Oit- N O oqddI ^ o o

o'd qoddI ^

CIN rHO qqddOON rHO qqo'd +^

NNc-co rHO OO

o'd +^

lOOi coco N O qqdd

rH *to N O O

to to N O o o

rHtOiOi N O O o o o o

to Oi OiOO rHO 0 q dd1 " U S I t-r

••r *J I rH <

tON rHO

t-N rHO ddI ^

com

OiOO tON rHO

Tf Oi tOOi t-N rHO

tOOi C-rH rHO NOi

C-rH rHO OOI

Ngi

toco OON rHO dd I coo coo coo

II II II

NO

II II II II

rHO iHO

2i +

II II O m

f-N tor drH Nr

rH^ + + O EC

o-o HZ 3 <is 3 e a a

OiV Oi SSE

g c;

uu . t-gco

•O to 00 00 - Z22

84
Table 13-20. Calculated contributions of independent variables to OD70, the dynamic modulus after H days moist curing followed by 8 weeks in laboratory air of Series O

concretes

Inde- pendent

variable

Range of variables

(percent)

Coeincients from eq 2

table ld-19

Calculated

contributions

to OD70

Calculated range of contributions to OD70

Oonst. = "ho. 50

Air-content, NAE

cements. 0 to 4.5 -0.1716 0 to -0.77 0.77 CjA 1 to 15 —0.0267 —0.03 to —0.40 0.37 CaS 20 to 65 +0.0189 +0.38 to +1.23 0.85 C4AP 1 to 17 -0.0296 -0.03 to -0.50 0.47 SO3 1.2 to 3.0 +0.571 +0.69 to +1.71 1.02 K2O** 0 to 1.1 +0.124 0 to +0.14 0.14 APF *2500 to 5500 -0.000135 -0.34 to -0.74 0.40 Loss 0.3 to 3.3 +0.106 +0.03 to +0.35 0.32 MgO 0 to 5.0 +0.278 0 to +1.39 1.39 V** 0 to 0.1 -1.035 0 to -0.10 0.10

cm^/g.

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

Equations 3 and 4 were calculated using the

major oxides instead of the potential compounds

as in eqs 1 and 2. The S.D. values were about the same in both instances. In eqs 4A and 4B Si02

and Fe203 had coef./s.d. ratios of less than 1.0 in

addition to APF, Loss, Cu, and Zr as in eqs 2A

and 2B.

A corresponding series of equations for the

concretes made with NAE cements is presented

in table 13-27. The independent variables, their

coefficients, and the coef./s.d. ratios were generally in good agreement with those in table 13-26

where the AE cements were included. In the

equations calculated for the "odds" and "evens"

(eqs 2A, 2B, 4A, and 4B) Fe203 and Loss had

coef./s.d. ratios of less than 1.0 with the smaller

groups of cements in one or the other of the pairs

of equations.

Using the independent variables of eq 2, table

13-27, and the ranges of these variables, calculations were made of the estimated contributions to the dynamic modulus at 98 days and the ranges

of these contributions. The calculated values are presented in table 13-28. Higher values for air

content, C3A and APF, and possibly C4AF, Ba,

and Cu were associated with lower values for dynamic modulus. Higher values for CS, SO.,

Loss, and possibly Zr were associated with higher

values for dynamic modulus after 28 days re- soaking.

6.4.2. Dynamic Modulus of Series A Concretes The frequency distribution of the dynamic

modulus of the Series A concretes (5 ± 1-in slump)

is presented in table 13-29. There was a broad

distribution of values and an overlapping of the

values obtained with the concretes made of the

different types of cement.

A series of equations for concretes made of AE

+ NAE cements is presented in table 13-30, indicating the independent variables associated with

the dynamic modulus of the Series A concretes

after the 28-day resoaking period. Equation 1 shows that higher air content and higher w/c were

associated with lower dynamic modulus. Other

commonly determined variables, C3A, C3S, C4AF,

SO3, and APF were, as indicated in eq 2, also

associated with the dynamic modulus after 28

days resoaking. The reduction in variance was

highly significant. (See also table 13-57.) The

additional use of the trace elements Cu, Zr, Ti,

Rb, and Ba together with the commonly determined variables in eq 3 resulted in a further

significant reduction in variance.

Equations 3A and 3B calculated for the "odds"

and "evens" in the array of cements indicated

that the coef./s.d. ratios for fineness, Rb, and Ba

were less than 1.0 in one or the other of the equations for the smaller groups of cements.

A corresponding series of equations for the NAE

cements is presented in table 13-31. As indicated

in eq 1, the dynamic modulus after 28 days re- soaking was related to the air content and water/

cement ratio of the concrete made of the different

cements. The additional use of commonly determined independent variables, C3A, C3S, C4AF,

SO3, and fineness in eq 2 resulted in a significant

reduction in variance. (See table 13-57.) Use of

Table 13-21. Frequency distribution of cements with respect to AD70, the dynamic modulus of elasticity of Series A concretes

at 70 days (IJf days moist curing and then storing in laboratory air for 8 weeks)

Dynamic modulus of elasticity, 10' psi

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 Type cement to to to to to to to to to to to Total

3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 6.4

Number of cements

I 1 1 15 13 25 18 6 1 79 lA 1 3 3 1 8 H 4 8 19 12 14 8 2 67 iia 1 2 3 m 2 2 6 3 6 1 20 niA 1 2 3 IV, V 2 1 2 4 4 2 15

Total 1 3 1 9 28 42 43 40 18 8 2 195

85
K5

CO

IIi I s §

Si «

CO S « o<

Eh

Hiz;

OO do o o

do' o o d d o o o o o o

<o o rH O o«T-IO dd o

aico o o

to o o ^ N *

1HO dd

000 00

t-00 o o o o 0 o 00

dd1 ^ « 00

00 eo o o o o oq q dd

1-1 ITS ^ O O o q q dd

00O O q q d dI ^

00m o o 0 o 00q q d d1 ^

00 CO 00o o o o qqd d

O 10

>-l

O

OO 00o q d dI

i-HOO w o dd

N o dd o o o o

U5 00 ^ o dd o o

00 50 OM

dd

vno IC o

CO "a" CO 00

to o 00 00 00 o 00

1/5 q

d

d

000

fl<

q dd

ifl 00

Tj<

q dd

10 (M COM

fHO ddI

CO (N tHO dd

00 CO coco rtO ddI ^

ONoco

CO

q ddI ^

01 CO

(N

q

dd ^ 00

IMO

NOO tMOO

eg

q CJ

q dd dd

000

CO o o o

0>rt

0500

CJ o 00

qq

dd qqd d

00 CJ

tH o oqdd+^

CO 10

00 CJ

r-l

O

q o dd+^

CO 10

10 CO

rH

O qqdd+^

COO) N o 00dd

00

TP CO

CO o o o ddI

«0 00

CO to

CO o o o ddI

1-t o COiH O O d d

t>00

CO o 00

ddI ^

000

COOl

COd

4-^

coco

CO t- OHM01 10 I ^

CO

O CO ^

10 iH

d iH I ^ I -

00 o 00

OJ 00 00

<X> 1-1 00 COtH

tO

rl

O

U3 (O 00 00 o oI ^ 00I ^ 0 o1 ^ 00

1-1 o o dd dd

(N CO

CO to w d < to

Tj< tr- co-^P CO ai

iri

d

CO o

00 o d d

(N

O

<o o < «

CO lO

in o to 1-1

li II

CO t>

lo

d

<1 oi

rH CO »H +

II II +II II

<1 oi

II II

CO

CJiH U5C0 CJi-< OiCO

CO iH ^ Tf lA-rf Oi iH (O^ r^ CJ COi-H CO rH CJ CJ CO CJ 00 00 00 00 0000

CJ « 0 o o o o o q o dd1 ^

00 CJ qi-< dd

CJ 00

CO

q dd

CJO

COCO

rH

q ddI ^

CO 00

CO

COO

000s 010

oico

rH o CJ

O dd ddf CO

OS o

OCJ rHO

"trH

CO rH rH

tc

a > a < 5

<yc c0)

B

<D

J

a s e .2

a, 0) Q> 4J u V u cs

rHCJCO > SSS § O O O r 3 ZZZ *

86
Oi -TP TJ* 00

00 ai irt in CO 00 00

od in oi u?

ood d

qq

d

d o o

00

CO tH CO rH o o o o o o o d

to CM

COo o o o ddI ^ o

00 CO q o d d

00

00 CO o o o oo o o o o o o o o o o o o ^ q dd^ o o o o o o o q q dd

00 CO q q d d

9)00 O O O O o o o oNOO

00 CO o o o o o o o o

t- CO ooo oo q q ddI ^

COt^ r-(00 CO to O O O .-4 O O O O q q q q dd dd

CO e

Sv » e ^s

00 if5 WOOO d d

MOO

00 00

04 o d d o o oo oo o o o o oo o :>

00 00

CO lO

lO

O

dd o d d

ooo

oatin o d dN vn

Tj*

q

dd

rHinO

do*

U5 t-O

tr- tco q dd

in 00 « CO

•H

O r^q dd

c-co d COo

CO o^co

(NO o o o o o o

^t£> OlrH

O-^f OlO

COO coq d d

00 OS 00 q q do ^ SC» iH

O CO o ^ ^

(NO cjq dd dd I - I

OSCO OOM

r^oO rHOO

COO CO

O

q

O

qq

dddd qqddI ~- qqdd

r-tin 00 (N ^ O o q d d

qq

dd

t> CO

iH

O

qq dd

-^00

CO

i-H

O

q

q

d

d

Tj"

O

CO

O o o

;d o

cot>

CO o o o

COOl o ^ o o

ooo

CO o o o o o M in d ^

COOi

to

COCO coo

C- lO

O iH in rH in rH

rH

O

O 04

in CO

in .-H I ^

CC CO q rH

in rH I ^

C003O CO

in in t- o 00 C- CO CO

00 t- CON qqddIOJCO oo

M CO

OJ

t>t>

rH CO inoj

00 ai

O) CO

rH

O

t> in

CO o

C- CO

rH

O

OOO o OOI ^ O Tj* OICO

Tt« OJ rHO ddI ^

oco

t- CO

in oj ^00 So ^ CO CO

rH

O ^ O

in

q

"<td

CO OJ N O rH 00 o —< a CO

CO in

rH «

00 t>

COlO

CO CO

t> o o Tt< O CD O CO o

II II

rHO

to OJ Tt* .-1 in o t-00

rH

rH ' rH Ln rH

rH - + 4-

eo

tHB

>J

PQ<

Eh HZ < a 03 0-6 < 03

•ooo o o o< CO

22 S s e .2 u „ a

tOOO -0 o o Z2

87
Table 13-24. Calculated contributions of independent vari- ables to AD70, the dynamic modulus after lU days moist curing followed by 8 weeks in laboratory air of Series A

concretes

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 5 contributions contribuvariable (percent) table 13-23 to AD70 tions to AD70

Const. = -1-6.87 Air-content, NAE

cements- 0 to 4.5 -0.1517 0 to -0.68 0.68 w/c 0.6 to 0.7 -5.536 -0.33 to -0.39 0.06 CaA 1 to 15 —0.0336 —0.03 to —0.50 0.47 CsS 20 to 65 -1-0.0184 -1-0.37 to +1.20 0.83 CiAF 1 to 16 -0.0318 -0.03 to -0.51 0.48 SOi 1.2 to 3.0 H-0.538 -1-0.65 to +1.61 0.96 KaO 0 to 1.1 -1-0.282 0 to +0.31 0.31 APF** *2500 to 5500 -0.000075 -0.19 to -0.41 0.22 Loss 0.3 to 3.3 -1-0.784 +0.24 to +2.59 2.35 MgO 0 to 5.0 -1-0.314 0 to +1.57 1.57 Li** 0 to 0.02 -f-9.09 0 to +0.18 0.18

*cmVg.

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

the trace elements Cu, Zr, Ti, Rb, and Ba as independent variables in eq 3, caused a further

significant reduction in variance, although the

coefficients of the individual trace elements were

not highly significant.

Equations calculated for the "odds" and "evens"

in the array of cements, eqs 3A and 3B, indicated

instances where fineness, Zr, Rb, and Ba had

coef./s.d. ratios less than 1.0 in eq 3A.

The use of the major oxides in eqs 4, 5, and 6

resulted in S.D. values which were nearly the same

as those obtained in eqs 2 and 3. The coef./s.d.

ratio for Fe203 was greater than 1.0 in eq 5 but was less than 1.0 in eq 6. In eqs 5A and 5B calculated for the "odds" and "evens" the coef./s.d.

ratios were less than 1.0 with Si02, CaO, fineness,

Cu, Rb, and Ba in one or the other of the smaller

lots of cements.

Using the independent variables of eq 3 of table

13-31, and the ranges of these variables, calculations were made of the estimated contributions to the dynamic modulus of the Series A concretes

after 28 days resoaking and the ranges of these

contributions. The calculated values are presented

in table 13-32.

Higher values for air content, w/c, C3A, C4AF,

were associated with lower values for dynamic

modulus. Higher values for SO3 and possibly C3S

and Zr were associated with higher dynamic modulus values. Variations of air content, w/c and SO3

had the greatest calculated range of contributions

to AD98.

6.5. Effect of Drying on Dynamic Modulus

6.5.1. Ratio of OD70 to OD14 for Series O Concretes

(OE70/14)

The dynamic modulus was determined at 14

days after moist curing and again after drying in

air for an additional 8 weeks. The frequency dis- tribution of the ratios of dynamic modulus after

drying to that before drying of the Series 0 concretes is presented in table 13-33. Concretes made

of nine of the cements had higher dynamic modulus after the drying period but the majority of the

concretes had lower values after the drying period

than after the original 14 days in moist air. There was a broad distribution of results and an over- lapping of the ratios for the concretes made of

the different types of cement.

A series of equations for concretes made of AE

+ NAE cements is presented in table 13-34 indicating the independent variables associated with

the dynamic modulus ratio. The use of commonly

determined variables C3A, Na20, SO3, APF, Loss,

and MgO in eq 1 resulted in a highly significant

reduction in variance. (See table 13-57.) The

additional use of the trace elements Rb, Zr, and

Mn in eq 2 resulted in a reduction of variance,

significant at the 5.0-percent level. Calculations made for the "odds" and "evens"

in the array of cements indicated that the coef./

s.d. ratios for MgO, Rb, and Mn were less than

1.0 in eqs 2A or 2B.

Equations 3 and 4 were calculated using CaO

and AI2O3 instead of C3A and including also the

air content. The use of the commonly determined

variables resulted in a highly significant reduction

in variance. The additional use of the trace ele- ments as independent variables resulted in a

Table 13-25. Frequency distribution of cements with respect to OD98, the dynamic modulus of elasticity of Series 0 concretes

after storage of air-dried specimens in water for 28 days

Dynamic modulus of elasticity, 10' psi

3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 Type cement to to to to to to to to to to Total

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

Number of cements

I 3 16 35 19 8 1 82

868

320

315

lA 1 3 3 1

1

1 II 101 29 22 5 1 IIA 1 III.. 8 9 3 IIIA 1 1

1

1 IV, v 4 6 4 Total 1 3 5 5 3 32 78 54 16 2 199

88
0>0) oo

CD lO

C- (N o o

o o ooo o

d o'

I ~-'

atcoco ^o

o'd +^

tow

o'd

CO 00

CD 00 CON d d

o q do

I "

00 Tj* t- N

o o

o o o o

o o

d d

CO

CO

C- CO dd

I ^

oq

d d

ai IN o o

o o o o o o

tr- CD CON

7^

cot- d d

q q

d d

CO (N

COo o

o o

o o

o o

c-co

U5 CJ

as o oco

CO O) d d

TP C4 qqdd

o o o o

o o o o

CO

1^5 (M

IT) ^

Tt« (M O O

CD a> th o lO CO o

CO °o iC d d d d

CO Tf X oc

Tf N

q q

d d

CO CO coco q q dd

O Tf 00 CJ o o

o o

o o

o o

o o o o o o

00 ffl OliM CO o o o o

o o o o o o o o

q q q q d d d d d d

CO TP

00 CO T-4q dd

la TP wq

d d

Ol CO CO o o oo

-#1-1 com ^ O U5 i-*q «

q

dd dd

CO CO q q dd

I ^

CD iH o o

qqd d

CO CO CO oi N O

q q dd

q q d d

I

q q

d d

I ^

t>U3

<N CO

CO ^

o o

u5

CO o

q q dd

q q d d

I ^

CO Tp 00 Tp oo

O t- CD

TP 1-tO

tr- (N lO CO q q qq d d d d

aico

TP a>

Tp -H O o

CO tC- X

tr-fM o o

00 O CO t- CO(M O iC CO w CO i-l q q o o dd+^ o o

4-^

U5CO w o q q dd

I

ffsco iC 1-1 oo

qqdd+^

CJ TP ^o

qqdd

I ^

qqdd

I ^

OiC

to ^ oo

qqdd+^

1-IO qqdd

I ^

o o dd

I ^

to irt Ol 00

CO 1-1 oo

M CO

TP (M o o

q q dd dd

CO lO

—I O qqdd

COO

t- CO

1-1 o

q q

d d

CJ I Tf o oo

I ^

ON t-N lOO tPCD X CO OCO CO i-i OlO C- CD CC Qi OliO Xm CD CO

TP o o mo coo eo o cm o ico

iH q i-H q rH q i-^q wq i-h q .-i o dd dd dd dd dd dd dd

04

04

U5 d

O m

la o

II II

U5 O U50 TfO

II II

O oi

O

O oi O m

>H 1-1 N

(TO HZ

ji C fl c

0^ 0) a; •2 6 S E

*r oj 0) 0)

rt o t) c)

. Oi O Oi

tr- a>x

03 ^ ^""(N CO* O +j +,» +j rX O O O

fc3

CO

s S

i-2

O

s

o

s

o

a

CD<

00 t- O cco w dd+^

ooo dd

I ^

C-O ijxji q q q q dd dd

o in X 04 O O

o o

o o o o

X 04 o o

o o

o o

o o

t-TP

05C0 ^ q dd

CO CD X CO

«tp iC ^ d

X irt COtr- X CO dd

I ^

icco

t- CO X 03 q q

d d

lO o

ai CO o o

o o o o

o o

Tp04

"Jdd

d d

4-^

xco

iOtP dd

I ^

o

t:- O

^CO O O

O O

OO

O

OO

OOO)

todd

U5«

-id o o

00 -H If ii5 »f 00 OCO

CO n t- ^ d d d d

coco

COO O

O lO O O

OO o

o o

oo

in M qqdd

o o

o o

o o

o o

ocooo

IN q

d d

NOO X M qqd dt-oo O CO OCO q q dd

I ^

CO -^O

Ol CO lO 11' O O o o

o o o o

o o o o

q q qq dd dd

CO-H COO

coco Oiia

»H q w q d d d d

NCO OO

00 in O 'H OO o o

CO

CO o eg o o

OU30

COIN qqd d

COOOdd

I -

<N CO

IJ>CC CO Oi q q dd q q

d d

X t- CO-H q q dd q q dd

1 -'

-HCO CON ooCOlA

CO 00 COM oo

•H CO -HO)

CO o qqdd+^

CO Oi

CO o

q q dd

lO(M -H q q dd oo

q q dd

I

o o o

OS o

CO t-

-H O

q q

d d

I

^eo

O) X

o o o o

CO eg IM CO

CO w oo

qqdd

eg U5

CO i^

CO -H o o o o oo

o o

q q

d d

X -H

-H o

o o

CO t> coin

-H o

o o

lOCOo o o

coco O CO

-H wo

CO -H ^CO

eg -H -H o

ej -Hq dd

eo -<r eg eg c-o ^fas

en CO coco cox -^cs cow cg-H cg-^ CO--" -HO -HO wo wo

o o

I ^ o o o o

I ^ o o

xeo XN

mo U30

Tfteg w

id d

q w

U5 d

lOoqd

II II II II II 11 II

o-o HZ

O n Qtj Qtj Qt3 O on Ob Ob a-6 O a w w eg

c c c J::

i> o o .

41s £0) 0)e I

y cj cj a

O O O ZZZ .

89
Table 13-28. Calculated contributions of independent vari- ables to OD98, the dynamic modulus of Series 0 concretes

after air dried specimens were stored in water for 28 days

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 2 contributions contribuvariable (percent) table 13-27 to OD98 tions to OD98

Const. = +5.18

Air-content, NAE

cements. 0 to 4.5 -0.1293 0 to -0.58 0.58 CsA 1 to 15 -0.0158 -0.02 to -0.24 0.22 CaS 20 to 65 +0.00632 +0.13 to +0.41 0.28 C4AF 1 to 16 -0.0124 -0.01 to -0.20 0.19 SO3 1.2 to 3.0 +0.197 +0.24 to +0.59 0.35 APF *2500 to 5500 -0.000081 -0.20 to -0.45 0.25 Loss 0.3 to 3.3 +0.0397 +0.01 to +0.13 0.12 Ba 0 to 0.02 -0.702 Oto -0.14 0.14 Cu 0 to 0.05 -2.47 0 to -0.12 0.12 Zr 0 to 0.5 +0.608 0 to +0.31 0.31

*cm2/g.

reduction of variance significant at the 5.0-percent

level. A corresponding series of equations calculated

for the Series 0 concretes made of NAE cements

is presented in table 13-35. The coefficient and

coef./s.d. ratio for air content of concretes made

of NAE cements were greater in magnitude and

appeared somewhat more significant than in the

previous table where the AE cements were in- cluded although there were instances (eqs 2A and

4A) where the coef./s.d. ratio was less than 1.0. The coef./s.d. ratios of CaO, fineness, Rb, Zr, and

Mn were also less than one in 1.0 or both of the

equations calculated for the "odds" or "evens" in the array of cements.

Using the coefficients of the independent variables of eq 2, table 13-35, and the ranges of these

variables, computations were made of the estiTable 13-29. Frequency distribution of cements with respect to AD98, the dynamic modulus of elasticity of Series A concretes

after storage of air-dried specimens in water for 28 days

Dynamic modulus of elasticity, 10' psi

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 Type cement to to to to to to to to to to Total

4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0

Number of cements

I... 4

4

2

22 35 14 2 1 1 79

867

320

315

lA 1 3

II 10

2

5

12

25 22 8 IIA.. 1 III 3 11

13

1 IIIA 1 IV, V 1 9

Total 1 1 4 11 42 72 51 10 2 1 195

Table 13-30. Coefficients for equations relating AD98, the dynamic Young's modulus

NAE cements were stored in water for 28

Eq. No. Note 10« psi Const.

Air content w/c CsA CoS C4AF CaO

1..

2..

3..

3A

3B

4..

6..

5A

5B

6..

AD98

s.d. AD98

s.d. AD98

s.d. AD98 (odd)

s.d. AD98 (even)

s.d. AD98

s.d. AD98

s.d. AD98 (odd)

s.d. AD98 (even)

s.d. AD98

s.d.

= +8.814

= (0.450)

= +9.501

= (0.455)

= +9.589

= (0.445)

= +11.170

= (0.728)

= +8.108

= (0.573)

= +10.216

= (0.888)

= +8.672

= (0.721)

= +9.822

= (1.180)

= +7.181

= (1.018)

= +9.699

= (0.872)

-0.1134

(0.0080) -0.1298

(0.0083) -0.1285

(0.0080) -0.1504

(0.0116) -0.1033

(0.0119) -0.1303

(0.0083) -0.1242

(0.0077) -0.1427

(0.0118) -0.1026

(0.0111) -0.1287

(0.0081)

-5.499

(0.687) -6.754

(0.717) -6.795

(0.694) -9.106

(1.148) -4.633

(0.892) -6.739

(0.718) -6.562

(0.687) -8.490

(1.182) -4.726

(0.875) -6.693

(0.702)

-0.0146 +0.00468 -0.0194

(0.0043) (0.00159) (0.0053) -0.0179 +0.00475 -0.0166

(0.0043) (0.00153) (0.0052) -0.0192 +0.00524 -0.0268

(0.0079) (0.00221) (0.0081) -0.0190 +0.00445 -0.0097

(0.0056) (0.00220) (0.0079)

Note 1, 173 cements, Avg. = 5.080 X 10» psi, S.D. = 0.2146 X 10» psi Note 2, 87 cements Note 3, 86 cements

Coef./s.d. ratio less than 1. **Coef./s.d. ratio less than 1 in "odds" or "evens".

+0.0130

(0.0092) +0.0262

(0.0084) +0.0276

(0.0131) +0.0263

(0.0114) ** +0.0181

(0.0091)

90
mated contributions to the dynamic modulus ratio

and the calculated range of these contributions.

The results of these calculations are presented in table 13-36. Higher C3A, and possibly Na20,

fineness, and Zr were associated with lower values

for the OE70/14 ratio. Higher values for SOs and

loss on ignition were associated with higher values

for the ratio.

6.5.2. Ratio of OD70 to OD14 for Series A Concretes

(OE70/14)

The frequency distribution of the ratio of the

dynamic modulus of Series A concretes after drying for 8 weeks to the dynamic modulus after the

initial 14-day moist curing is presented in table

13-37. Twelve of the concretes made of the 195

cements had higher dynamic modulus values after

drying in laboratory air whereas most had lower

values after than before the dry storage. There was a broad distribution of values and an over- lapping of values obtained with the different

types of cement.

A series of equations for concretes made of AE

-\- NAE cements is presented in table 13-38 to

indicate the variables associated with the dynamic

modulus ratio of the Series A concretes. The use

of the commonly determined variables, C3A,

C4AF, SO:,, Na,0, MgO, APF, and Loss in eq 1 resulted in a highly significant reduction in vari- ance. (See table 13-57.) The additional use in eq

2 of the trace elements Co, Rb, and Mn resulted

in a reduction of variance significant at the 5.0- percent level although none of the coefficients for the individual trace elements was highly significant.

The use of CaO, AI2O3 and Fe203 together with

the other commonly determined variables in eqs

3 and 4 resulted in S.D. values which were about

the same as those obtained in eqs 1 and 2 where

the calculated potential compounds were used.

Equations calculated for the "odds" and "evens"

in the array of cements indicated that the coef./

s.d. ratios were less than 1.0 for C4AF, CaO, Fe203,

Co, Rb, and Mn in one or the other of the smaller

lots of cement. (See eqs 2A, 2B, 4A, and 4B.)

A series of equations calculated for the Series A

concretes made of NAE cements is presented in table 13-39. As was the case with the Series 0

of elasticity in 1 0^ psi after air-dried specimens of Series A concretes made of AE +

days, to various independent variables

SiOs AUO3 FezOs SO3 APF Cu Zr Ti Rb Ba S.D.

0.1423

+0.216

(0.035) +0.204

(0.035) +0.254

(0.053) +0.129

(0.049) +0.189

(0.038) +0.200

(0.037) +0.251

(0.060) +0.134

(0.052) +0.197

(0.037)

-0.000053

(0.000023) -0.000051

(0.000022) -0.000073

(0.000033)

* -0.000008

(0.000034) -0.000055

(0.000023) -0.000049

(0.000023) -0.000063

(0.000034)

* -0.000005

(0.000033) ** -0.000052

(0.000023)

0.1230

-3.02

(1.08) -3.89

(1.64) -2.42

(1.51)

+0.541

(0.222) +0.450

(0.250)

' +0.733

(0.571)

-0.165

(0.080) -0.161

(0.099) -0.183

(0.150)

+ 8.60

(5.04) *+8.15

(8.16) +11.53

(6.59)

-0.428

(0.284) -0.644

(0.428)

* -0.254

(0.455)

0.1166

0.1206

0.1085

-0.0459

(0.0163) -0.0280

(0.0155) -0.0288

(0.0225)

* -0.0187

(0.0225) ** -0.0405

(0.0159)

-0.0815

(0.0197) -0.0701

(0.0190) -0.0718

(0.0312) -0.0647

(0.0247) -0.0853

(0.0193)

-0.0469

(0.0150) 0.1231

-3.69

(1.05) -4.66

(1.75) -2.35

(1.33) -2.81

(1.11)

+0.547

(0.224) +0.475

(0.263) +0.706

(0.566) +0.479

(0.223)

-0.189

(0.081) -0.171

(0.105) -0.194

(0.144)

+8.93

(5.10) +8.70

(8.66) +11.50

(6.55) **+8.04

(5.11)

-0.450

(0.289) -0.601

(0.462)

* -0.219

(0.449) ** -0.489

(0.289)

0.1177

0.1266

0.1078

** -0.0314

(0.0153) 0.1182

91
Table 13-31. Coefficients for equations relating AD98, the dynamic Young's modulus

cements were stored in water for 28 d

Eq. No. Note 10« psi Const. Air content w/c

AD98 = +8.749 -0.1075 -5.412

s.d. (0 477) (0.0156) (0.722) AD98 = +9.703 -0.1396 -7.118

s.d. (0.494) (0.0154) (0.778) AD98 +9.712 -0.1276 -7.051

s.d. (0.475) (0.0150) (0.743) AD98 (odd) = +10.001 -0.1215 -7.531

s.d. (0.609) (0.0204) (0.971) AD98 (even) = +9.274 -0.1391 -6.315

s.d. (0.684) (0.0203) (1.054) AD98 = +10.216 -0.1397 -7.101

s.d. (0.924) (0.0155) (0.780) AD98 = +9.565 -0.1311 -6.951

s.d. (0.908) (0.0152) (0.755) AD98 (odd) +8.161 -0.1195 -7.667

s.d. (1.212) (0.0200) (0.961) AD98 (even) +10.611 -0.1495 -5.971

s.d. (1.382) (0.0223) (1.148) AD98 +8.527 -0.1196 -6.850

s.d. (0.731) (0.0141) (0.727)

CaA CsS C4AF

1..

2..

3..

3A

3B

4..

5..

5A

5B

6..

-0.0137

(0.0044) -0.0173

(0.0044) -0.0266

(0.0067) -0.0142

(0.0057)

+0.00463

(0.00164) +0.00468

(0.00157) +0.00329

(0.00220) +0.00410

(0.00237)

-0.0195

(0.0054) -0.0160

(0.0053) -0.0294

(0.0084) -0.0081

(0.0069)

Note 1, 162 cements, Avg. = 5.112 X 10^ psi, S.D. = 0.1716 X 10« psi. Note 2, 81 cements

*Coe{./s.d. ratio less than one. **Coef./s.d. ratio less than one in "odds" or "evens".

Table 13-32. Calculated contributions of independent vari- ables to AD98, the dynamic modulus of Series A concretes

after the air-dried specimens were stored in water for 28 days

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 3 contributions contribuvariable (percent) table 13-31 to AD98 tions to AD98

Const. = +9.712

Air-content, NAE

cements. 0 to 4.5 -0.1276 0 to -0.57 0.57 w/c 0.6 to 0.7 -7.051 -4.23 to -4.94 0.71 CaA 1 to 15 -0.0173 -0.02 to -0.25 0.23 CS 20 to 65 +0.00468 +0.09 to +0.30 0.21 CiAF 1 to 16 -0.0160 -0.02 to -0.26 0.24 SO3 1.2 to 3.0 +0.209 +0.25 to +0.63 0.38 APF** *2500 to 5500 -0.000042 -0.10 to -0.23 0.13 Cu - 0 to 0.05 -3.09 0 to -0.15 0.15 Zr 0 to 0.5 +0.581 0 to +0.29 0.29 Ti 0 to 1.0 -0.189 0 to -0.19 0.19 Rb** 0 to 0.01 +8.10 0 to +0.08 0.08 Ba** 0 to 0.02 -0.460 0 to -0.01 0.01

*cmVg.

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

concretes, the coefficients of the air content of the

concretes made with NAE cements are probably

significant, which was not evident when the AE

cements were included. The use of commonly

determined variables in eqs 1 and 3 resulted in a

highly significant reduction in variance. (See table

13-57.) The additional use of the trace elements

Co, Rb, and Mn in eq 2 resulted in a reduction of variance significant at the 5.0 percent probability

level. In eq 3, CaO had a coef./s.d. ratio greater

than 1.0 but the ratio was less than 1.0 in eq 4; therefore an evaluation of the reduction of vari- ance was not made.

With the use of the coefficients of the independent variables of eq 2 table 13-39 and the ranges

of these variables, computations were made of the

estimated contributions to the AE70/14 ratio. These computed values are presented in table

13-40 together with the calculated ranges of the

contributions. Higher values for C3A, Na20, and

probably air content, and fineness were associated

92
of elasticity in 10^ psi after air dried specimens of Series A concretes made of NAE

ays, to various independent variables

SiOz FesOj SO3 APF Cu Zr Ti Rb Ba S.D.

0.1448

+0.224

(0.035) +0.209

(0.035) +0.267

(0.050) +0.176

(0.050) +0.201

(0.039) +0.209

(0.039) +0.277

(0.052) +0.129

(0.059) +0.210

(0.038)

-0.000045

(0.000024) -0.000042

(0.000023)

* -0.000009

(0.000036) -0.000045

(0.000030) -0.000046

(0.000024) -0.000043

(0.000024)

* -0.000003

(0.000035) -0.000058

(0.000033)

** -0.000040

(0.000023)

0.1240

-3.09

(1.12) -5.24

(1.61) -2.13

(1.49)

+0.581

(0.224)

* +0.204

(1.884) +0.639

(0.217)

-0.189

(0.083) +0.169

(0.137) -0.459

(0.116)

+8.10

(5.22) *+7.02

(7.03) +10.26

(7.31)

-0.460

(0.288)

* -0.169

(0.870)

* -0.058

(0.323)

0.1168

0.1134

0.1081

-0.0428

(0.0169) -0.0367

(0.0164)

* -0.0006

(0.0212) -0.0687

(0.0275) ** -0.0227

(0.0159)

-0.0759

(0.0205) -0.0802

(0.0199) -0.0667

(0.0233) -0.1052

(0.0350) -0.0633

(0.0196)

-0.0469

(0.0156) -0.0293

(0.0160) -0.0299

(0.0226) -0.0333

(0.0228)

0.1243

-2.85

(1.15) -5.92

(1.62) *-0.55

(1.60) -3.80

(1.06)

+0.497

(0.225)

* +0.670

(1.669) +0.465

(0.231)

** +0.591

(0.225)

+8.05

(5.32) +9.29

(7.10) +11.48

(8.03) +8.11

(5.26)

-0.524

(0.296)

* -0.461

(0.856)

* -0.210

(0.352) ** -0.517

(0.292)

0.1189

0.1120

0.1181

** -0.225

(0.084) 0.1174

Table 13-33. Frequency distribution of cements with respect to OE 70/H, the ratio of dynamic modulus of Series 0 concretes determined after 8 weeks in laboratory air divided by the values after the original H days of moist curing

Dynamic E ratio

0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 Type cement to to to to to to to to to to to Total

0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04

Number of cements

I 2 4 11 10 13 12 17 7 6 82 lA 2 3 2 1 8

II 2 2 7 5 8 16 9 8 8 1 2 60 IIA 1 1 1 3

III 1 1 2 2 2 5 5 20

IIIA 1 1 1 3 IV, V 2 1 2 4 1 3 2 15

Total 4 6 19 20 25 36 34 24 22 6 3 191

93
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t- .H iniH o o o o oo oo

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O

OO o o o o q q d dI

00 (N

tCO i-H qqddq q d d

CO CD

CO 'tH OJ CO o o qqddI

OOi-t ooq dd+^

II II

ooq d d

iH tr1-1 oa qqdd o o w

d 1-3

d i-Hd

II II II II II II

•ao o

c- oc- ot- W-d O 03 H-d O 03 H-d O 03 W-d O 03 W-d O 03 H-d O 03 w-d O 03

1-1 rH 04

qq

dd

•flIiH t- O

Oi-^ ooo o o o q q d d O CO O04

t> rH qqdd

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94
Table 13-36. Calculated contributions of independent vari- ables to OE70/H, the ratio of dynamic modulus of Series O

concretes after drying in air for 8 weeks divided by the

. dynamic modulus after the original 1 l^-day moist curing

T H pendant

vari&blc

JKange ot variables

(percent)

L/Oetncients from eQ 2

(.yalcuiated contributions

LU \J 111 t\J/ J. ft

Calculated range of contributions to

CaA 1 to 15 —0.00573 —0.006 to —0.086 0.080 NazO 0 to 0.7 0.0343 U CO —U.U^4 0 024 SO3 1.2 to 3.0 +0.0719 0.130 APF *25bo to 5500 -o!ooooi7i -0.043 to -0.094 o!o5i Loss 0.3 to 3.3 +0.0223 +0.007 to +0.074 0.067 MgO**.-- 0 to 5.0 +0.00269 0 to +0.013 0.013 Rb** 0 to 0.01 -1.37 Oto -0.014 0.014 Zr 0 to 0.5 -0.136 0 to -0.068 0.068 Mn** 0 to 1.0 +0.0288 0 to +0.029 0.029

Air-content, NAE

cements0 to 4.5 -0.01012 0 to -0.046 0.046

*cmVg.

**Coefiicient of doubtful significance as coef./s.d. ratio was less than 2.0.

with lower values for AE70/14. Higher values for

SO;i and loss on ignition were associated with

higher values for the AE70/14 ratio.

6,6. Effect of Rewetting on Dynamic ModuluM

6.6.1. Ratio of 98-Day (Wet) to 70-Day (Dry) Dynamic

Modulus of Series O Concretes

After drying in laboratory air for 8 weeks, the

dynamic modulus was determined (total age 70

days). The specimens were then placed in water

and the dynamic modulus was again determined

after 4 weeks (total age 98 days). The ratio of the

dynamic modulus values OE98/70 was calculated

and the frequency distribution of this ratio for the Series 0 concretes is presented in table 13-41.

The concretes made with all of the cements showed some increase in dynamic modulus due to the

Table 13-37. Frequency distribution of cements with respect to AE 70/IJ^, the ratio of dynamic modulus of Series A concretes determined after 8 weeks in laboratory air divided by the values after the original H days of moist curing

Type cement

Dynamic E ratio

0.82

to 0.84

0.84

to 0.86

0.86

to 0.88

0.88

to 0.90

0.90

to 0.92

0.92

to 0.94

0.94

to 0.96

0.96

to 0.98

0.98

to

1.00

1.00

to 1.02 Total

Number of cements

I 1 5 8 12

18

13

1 11

13

19

1 11

12

12

2

11

13

14

5 4

1 10

79

867

320

315

lA 2

II 3 IIA

3 4 6

III 2 3

13

5 2

14 IIIA

IV, V 1 1 1 1

Total 4 5 15 22 30 35 34 18 20 12 195

95
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CO N

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CO 00

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C<1 CO

COesq d d

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05 O

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coco

CO -"Ji CO Tj* qodd+^

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04 O

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I " I ^

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004 to q q 00 q dd dd +^

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01 to 00 CO 00 to TH.H 04OJ O04 O 1-1 o 1-1 O 1-1 o

=^5

Wt3 m-6 Wt3 H-d H-d H-d

EQ ^ ID ^ oi

tH ^ W

fl fl d Ji

<U O 0) a B B .2

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1-1 ;D irt C-OOOO

O V D V +j +J O

O O O
soaking. There was, however, a fairly broad dis- tribution of values and an overlapping of the

values obtained with the different types of cement.

A series of equations is presented in table 13-42

to indicate the independent variables associated

with the 98-day/70-day dynamic modulus ratio

of Series 0 concretes made with AE + NAE ce- ments. The use of air content, C3A, C3A/SO3, C3S,

C4AF, K2O, Loss, and MgO as independent variables in eq 1 resulted in a highly significant reduction in variance. With the additional use of the

trace elements Co, Li, Zr, and P in eq 2 there was

a further significant reduction of the S.D. value.

(See table 13-57.)

The use of CaO and SiOa together with AI2O3/

SO3 instead of the calculated potential compounds

in eq 3 also resulted in a significant reduction in variance. In eq 4 the use of the trace elements

caused a reduction of variance significant at the

ii.O-percent level. Equations calculated for the "odds" and "evens"

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

show instances where the coef./s.d. ratio was less than 1.0 for C4AF, K2O, MgO, Co, and P in one

or both of the equations for the smaller lots of cement.

A corresponding series of equations for the ratio

of dynamic modulus after to that before resoaking

for the Series 0 concretes made of NAE cements

is presented in table 13-43. The coefficients for the independent variables as well as the coef./s.d.

ratios were in reasonable agreement with those of

the previous table where the AE cements were

included.

Using the coefficients of the independent variables in eq 2 table 13-43 as well as the ranges of these variables, calculations were made of the

estimated contributions to the ratio of dynamicmodulus values after to that before resoaking and

the ranges of these contributions. The calculated

values are presented in table 13-44. Higher values

for air content and C3A/SO3 were associated with

higher values for the dynamic-modulus ratio. Higher values for C3A, C3S, and possibly K2O,

Loss, MgO, and Li were associated with lower

values for the dynamic-modulus ratio. Variations

of C3A, C3A/SO3 and C3S had the greatest effect on the calculated range of contributions to OE98/70.

6.6.2. Ratio of 98-Day (Wet) to 70-Day (Dry) Dynamic

Modulus of Series A Concretes The frequency distribution of the ratio of dynamic modulus after to that before resoaking for

Series A concretes is presented in table 13-45.

Concretes made of all of the cements increased in dynamic modulus with the increase ranging from

less than 5 to more than 40 percent. There was an

overlapping of the values obtained with the dif- ferent types of cement.

A series of equations indicating the independent

variables associated with the OE98/70 dynamicmodulus ratio of Series A concretes made with

AE + NAE cements is presented in table 13-46.

The use of the air content, C3A, C3S, C^AF, SO3,

K2O, Loss, and MgO in eq 1 resulted in a highly

significant reduction of variance. (See table 13-.57.)

With the addition of C3A/SO3 as an independent

variable in eq 2 the sign of the coefficient for C:;A became negative and the coef./s.d. ratio for SO.-, became less than 1.0. Deleting SO3 as an independent variable in eq 3 resulted in higher coef./

s.d. ratios for both C3A and C3A/SO3. The interrelation between these independent variables is obvious and has been discussed in previous sections. The use of the trace elements Li, P, and Co

in eq 4 together with the commonly determined

variables resulted in a significant reduction in variance. (See table 13-57.) Equations 5 and 6 were calculated using CaO and SiOo in place of C3A, C3S, and C4AF. There was a significant re- duction in variance in both equations.

In equations calculated for the smaller lots of cement, C4AF, P, and Co had coef./s.d. ratios less than 1.0 in eq 4B, and P and Co had coef./s.d.

ratios less than 1.0 in eq 6B.

With the use of only the NAE cements, equations were calculated to determine the variables

associated with the OE98/70 dynamic-modulus

ratio. The results are presented in table 13-47.

There was a reasonable agreement of the coeffi- cients and coef./s.d. ratios with those of the pre- vious table where the AE cements were included.

There were instances in the equations for the

"odds" and "evens" where air content, MgO, P,

and Co had coef./s.d. ratios less than 1.0 in the

smaller lots of cement.

Using the coefficients of the independent variables of eq 4 table 13-47, calculations were made

of the estimated contributions to the AE 98/70

dynamic-modulus ratio. These calculated values

together with the calculated ranges of contributions to the ratio are presented in table 13-48.

Higher values for C3A/SO3 and possibly air content, C4AF, and P were associated with higher

ratios. Higher values for C3A, C3S, K2O, and

possibly loss-on-ignition, MgO, and Li were asso- ciated with lower ratios. Variations of C3A, C3A/

SO3 and C3S had the greatest effect on the

calculated range of contributions to AE98/70.

6.7. Effect of 24-Hour Water Storage of AirDried Concrete on Dynamic Modulus

6.7.1. Ratio of 71-Day (24-Hour Water Storage) to 70- Day (Air-Dried) Dynamic Modulus of Series O Concretes The frequency distribution of the ratio of dynamic modulus after one day of soaking to that

of air-dried Series 0 concretes (OE98/70) is pre- sented in table 13-49. The concretes made with more than half of the cements decreased slightly

in dynamic modulus when the air-dried specimens were placed in water for 24 hours. Other specimens

showed a slight increase in dynamic modulus. As

indicated in tables 13-41 and 13-45, storage in

97
Table 13-39. Coefficients for equations relating AE 70/H, the ratio of dynamic Youn

curing) of Series A concretes made with NA

Eq. No. Note Const. Air content CiA C4AF CaO AI2O3 FesOa

1. 1

1

2

2

1

1

2

2

AE 70/14 = +0.930

s.d, = (0.027) AE 70/14 = +0.928

s.d. = (0.027) AE 70/14 (odd) = +0,946

s.d. = (0.045) AE 70/14 (even) = +0.917

s.d. = (0.038) AE 70/14 = +1.233

s.d. = (0,168) AE 70/14 = +0.932

s.d. = (0.027) AE 70/14 (odd) = +0.958

s.d. = (0.044) AE 70/14 (even) = +0.917

s.d. = (0.037)

-0.00802

(0.00289) -0.00708

(0.00291) -0.00772

(0.00491) -0.00637

(0.00406) -0.00817

(0.00291) -0.00815

(0.00288) -0.00986

(0.00468) -0.00674

(0.00393)

-0.00809

(0.00104)

-(r.00794

(0.00106) -0.00977

(0.00179) -0.00656

(0.00143)

-0.00198

(0.00132) -0.00234

(0.00134) -0.00414

(0.00238)

* -0.00122

(0.00179)

2

2A

2B._

3 , ... -0.00437

(0.00246) -0.0217

(0.0028) -0.0199

(0.0029) -0.0260

(0.0048) -0.0158

(0.0038)

+0.00429

(0.00375) +0.00491

(0.00339)

* +0.00298

(0.00589) +0.00565

(0.00457)

4

4A

4B

Note 1, 160 cements, Avg. = 0.9293, S.D. = 0.04321 Note 2, 80 cements

*Coef./8.d. ratio less than one.

Table 13-40. Calculated contributions of independent variables to AE70/H, the ratio of dynamic modulus of Series A concretes after drying in air for 8 weeks divided by the dynamic modulus after the original H days moist curing

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 2 contributions contribuvariable (percent) tabic 13-39 to AE70/14 tions to AE70/14

Const. = +0.928

Air-content, NAE

cements. 0 to 4.5 -0.00708 0 to -0.032 0.032 CsA 1 to 15 -0.00794 -0.008 to -0.119 0.111 C4AF**-.. 1 to 17 -0.00234 -0.002 to -0.040 0.038 SO3 1.2 to 3.0 +0.0732 +0.088 to +0.220 0.132 NasO 0 to 0.7 -0.0432 0 to -0.030 0.030 MgO**.... 0 to 5.0 +0.0038 0 to +0.019 0.019 APF *2500 to 5500 -0.0000169 -0.042 to -0.093 0.051 Loss 0.3 to 3.3 +0.0161 +0.005 to +0.053 0.048 Co** 0 to 0.01 +2.53 0 to +0.025 0.025 Rb** 0 to 0.01 -1.45 0 to -0.014 0.014 Mn** 0 to 1.0 +0.0392 0 to +0.039 0.039

*cmVg.

**Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

water for 28 days resulted in an increase of the

dynamic modulus with all the concretes. The inclusion of C3A, C3S, K2O, C3A/SO3, Loss,

and MgO as independent variables in eq 1 of table 13-50 resulted in a significant reduction of the S.D. value. The use of Co, Ni, Zr, and Mn

together with commonly determined variables in eq 2 caused an additional reduction in variance.

(See also table 13-57.) The use of SiOz and AI2O3/

SO3 in eqs 3 and 4 in place of C3A and C3S, MgO

and C3A/SO3 resulted in similar S.D. values.

In equations calculated for the "odds" and

"evens" in the array of cements, the coef./s.d.

ratio for C3S, K2O, MgO, Co, Ni, and Mn was less than 1.0 in one or the other of the equations for the smaller lots of cements.

A corresponding series of equations calculated

for the NAE cements is presented in table 13-51.

The independent variables, their coefficients and

coef./s.d. ratios were generally in agreement with

98
g's modulus of elasticity at 70 days {after drying in air) to that at H days (after moist E cements, to various independent variables

SOs

+0.0718

(0.0090) +0.0732

(0.0089) +0.0761

(0.0138) +0.0686

(0.0140) +0.0695

(0.0093) +0.0731

(0.0088) +0.0792

(0.0136) +0.0673

(0.0136)

NazO

-0.0451

(0.0148) -0.0432

(0.0147) -0.0334

(0.0269) -0.0456

(0.0194) -0.0492

(0.0150) -0.0542

(0.0160) -0.0341

(0.0288) -0.0588

(0.0205)

MgO

+0.0045

(0.0021) +0.0038

(0.0021) +0.0041

(0.0034) +0.0032

(0.0032)

APF

-0.0000166

(0.0000058) -0.0000169

(0.0000059) -0.0000156

(0.0000105) -0.0000170

(0.0000070) -0.0000147

(0.0000060) -0.0000154

(0.0000058) -0.0000160

(0.0000104) -0.0000150

(0.0000074)

Loss

+0.0168

(0.0051) +0.0161

(0.0051) +0.0179

(0.0090) +0.0148

(0.0070) +0.0138

(0.0053) +0.0142

(0.0051) +0.0157

(0.0096) +0.0138

(0.0068)

Co

+2.53

(1.74) +3.15

(2.32) *+1.23

(3.10)

+2.87

(1.75) +2.77

(2.29) *+2.63

(3.07)

Li

+1.45

(0.79) *+0.85

(1.26) +1.65

(1.07)

Rb

-1.45

(1.33) »-1.21

(2.06) '-1.29

(2.07)

Mn

+0.0392

(0.0208) +0.0483

(0.0283)

" +0.0333

(0.0360)

+0.0474

(0.0203) +0.0544

(0.0275) +0.0456

(0.0344)

S.D.

0.03088

0.03049

0.03212

0.03077

0.03100

0.03043

0.03209

0.03036

Table 13-41. Frequency distribution of cements with respect to OE 98/70, the ratio of dynamic modulus of Series 0 concretes determined after 4 weeks in water divided by the values after the previous 8 weeks in laboratory air

Dynamic E ratio

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 Type cement to to to to to to to to to Total

1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45

Number of cements

I 17 40

3

19

2

6

16

222

82

13

1

13

1

82

868

320

315

lA. II 9 2 ILA

III 8 5

3

1

1 IIIA . . rv, V 4 5 2 2 1

Total 8 35 74 46 26 6 4 0 1 199

99
Table 13-42. Coefficients for equations relating OE 98/70, the ratio of dynamic You

days {after drying in air) of Series O concretes made wit

Eq. No.

1-.

2..

2A

2B

3..

4..

4A

43

Note Const.

OE 98/70

s.d. OE 98/70

s.d. OE 98/70 (odd) ^ s.d. OE 98/70 (even)

s.d. OE 98/70

s.d. OE 98/70

s.d. OE 98/70 (odd)

s.d. OE 98/70 (even)

s.d.

+1.359

(0.043)

= +1.374

: (0.042) +1.362

: (0.054)

- +1.432

- (0.070) +1.799

(0.326)

= +1.922

= (0.321)

- +1.676

= (0.512)

= +2.032

= (0.406)

Air content

+0.00997

(0.00195) +0.01010

(0.00189) +0.01080

(0.00260) +0.01026

(0.00273) +0.00925

(0.00191) +0.00920

(0.00187) +0.00989

(0.00257) +0.00974

(0.00266)

CiA

-0.0173

(0.0025) -0.0178

(0.0024) -0.0163

(0.0039) -0.0197

(0.0031)

CaS

-0.00395

(0.00054) -0.00411

(0.00053) -0.00349

(0.00070) -0.00518

(0.00083)

CiAF

+0.00245

(0.00190) +0.00261

(0.00186)

* +0.00067

(0.00280)

* +0.00267

(0.00268)

CaO SiOj

-0.0206 +0.0269

(0.0044) (0.0036) -0.0227 +0.0280

(0.0044) (0.0036) -0.0177 +0.0251

(0.0068) (0.0053) -0.0268 +0.0340

(0.0058) (0.0049)

Note 1, 179 cements, Avg. = 1.152, S.D. = 0.06653 Note 2, 90 cements Note 3, 89 cements

*Coef./s.d. ratio less than one. Table 13-43. Coefficients for equations relating OE 98/70, the ratio of dynamic You

days (after drying in air) of Series O concretes made

Eq. No. Note Const. Air content CsA CaS CiAF CaO SiOj

1..

2-.

2A,

2B

3..

4..

4A

4B

OE 98/70 +1.351 +0

s.d. (0.045) (0 OE 98/70 +1.366 +0

s.d. (0.044) (0 OE 98/70 (odd) +1.285 +0

s.d. (0.054) (0 OE 98/70 (even) +1.506 +0

s.d. (0.078) (0 OE 98/70 +1.878 +0

s.d. (0.336) (0 OE 98/70 +2.006 +0

s.d. (0.330) (0 OE 98/70 (odd) +2.463 +0

s.d. (0.484) (0 OE 98/70 (even) +1.904 +0

s.d. (0.477) (0

-0.0172

(0.0026) -0.0179

(0.0025) -0.0157

(0.0040) -0.0192

(0.0034)

-0.00403

(0.00056) -0.00423

(0.00055) -0.00336

(0.00067) -0.00582

(0.00095)

+0.00261

(0.00196) +0.00278

(0.00190) +0.00649

(0.00251) "-0.00163

(0.00311) -0.0219 +0.0266

(0.0046) (0.0037) -0.0242 +0.0282

(0.0045) (0.0037) -0.0279 +0.0204

(0.0062) (0.0054) -0.0253 +0.0353

(0.0068) (0.0055)

Note 1, 167 cements. Avg. = 1.151, S.D. = 0.06643

*Coef./s.d. ratio less than one. Note 2, 84 cements Note 3, 83 cements

Table 13-44. Calculated contributions of independent variables to OE 98/70, the ratio of the dynamic modulus of Series 0 concretes after 28 days in water divided by the dynamic

modulus after the previous 8 weeks in air

Calculated

Inde- Range of Coefficients Calculated range of pendent variables from eq 2 contributions contribuvariable (percent) table 13-43 to OE98/70 tions to OE98/70

Const. = +1.366

Air-content, NAE

cements. 0 to 4.5 +0.0170 0 to +0.077 0.077 CaA 1 to 15 -0.0179 -0.018 to -0.268 0.250 CaS 20 to 65 -0.00423 -0.084 to -0.274 0.190 CiAF**... 1 to 17 +0.00278 +0.003 to +0.047 0.044 K2O 0 to 1.1 -0.0566 0 to -0.062 0.062 Loss 0.3 to 3.3 -0.0191 -0.006 to -0.063 0.057 MgO 0 to 5.0 -0.0065 0 to -0.032 0.032 C3A/SO3. . 0.4 to 10.1 +0.0340 +0.014 to +0.343 0.329 Co** . 0 to 0.01 -3.48 0 to -0.035 0.035

Li 0 to 0.02 -2.97 0 to -0.059 0.059 Zr** 0 to 0.5 +0.149 0 to +0.074 0.074 p** 0 to 0.5 +0.0422 0 to +0.021 0.021

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

those of the previous table where the AE cements

were included.

Using the coefficients of the independent variables of eq 2, table 13-51, calculations were made

of the estimated contributions to the OE71/70

dynamic modulus values. These calculated contributions are presented in table 13-52 together with

the calculated ranges of these contributions. Increases of air content, C3A/SO3, and Zr were

associated with increases of the ratio (OE71/70).

Increases of C3A, K2O, Loss, MgO, and possibly

Ni were associated with decreases of the OE71/70

values.

6.7.2. Ratio of 71-Day (24-Hour Water Storage) to 70- Day (Air-Dried) Dynamic Modulus of Series A Concretes

The frequency distribution of the ratio of dynamic modulus after 24 hovirs soaking to that of

100
ng's modulus of elasticity at 98 days (after soaking in water for 28 days) to that at 70

h AE ± NAE cements, to various independent variables

KiO Loss MgO

CaA AI2O3 SO3 Co Li Zr P S.D.

-0.0427

(0.0178) -0.0495

(0.0178) -0.0891

(0.0266)

* -0.0161

(0.0245) -0.0483

(0.0184) -0.0577

(0.0187) -0.0968

(0.0279)

* -0.0220

(0.0251)

-0.0227

(0.0065) -0.0232

(0.0065) -0.0141

(0.0097) -0.0316

(0.0092) -0.0255

(0.0074) -0.0271

(0.0074) -0.0157

(0.0116) -0.0362

(0.0099)

-0.0091

(0.0031) -0.0069

(0.0031)

* -0.0009

(0.0045) -0.0104

(0.0043) -0.0137

(0.0043) -0.0127

(0.0043)

* -0.0040

(0.0070) -0.0171

(0.0054)

+0.0351

(0.0043) +0.0339

(0.0042) +0.0286

(0.0068) +0.0376

(0.0054)

0.04420

-3.13

(2.35) —0.69

(3.54) -4.05

(3.17)

-2.53

(1.01) -3.06

(1.47) -2.23

(1.40)

+0.162

(0.084) +0.135

(0.090) +0.329

(0.230)

+0.0506

(0.0305) +0.1546

(0.0532)

* +0.0109

(0.0370)

0.04286

0.04243

0.04173

+0.0526

(0.0062) +0.0497

(0.0061) +0.0385

(0.0096) +0.0584

(0.0077)

0.04433

-2.72

(2.35) *+0.36

(3.46) -4.56

(3.14)

-2.51

(1.02) -3.22

(1.48) -2.03

(1.39)

+0.142

(0.084) +0.128

(0.091) +0.262

(0.227)

+0.0419

(0.0307) +0.1458

(0.0535)

* +0.0031

(0.0366)

0.04328

0.04284

0.04152

ng's modulus of elasticity at 98 days (after soaking in water for 28 days) to that at 70

with NAE cements, to various independent variables

K2O Loss MgO

CaA

SO3

AI2O3 SO3 Co Li Zr P S.D.

-0.0461

(0.0187) -0.0566

(0.0189) -0.0894

(0.0260)

* -0.0276

(0.0281) -0.0524

(0.0193) -0.0657

(0.0198) -0.1127

(0.0284)

* -0.0257

(0.0292)

-0.0192

(0.0068) -0.0191

(0.0067) -0.0169

(0.0088) -0.0223

(0.0107) -0.0223

(0.0076) -0.0233

(0.0076) -0.0278

(0.0108) -0.0244

(0.0118)

-0.0091

(0.0032) -0.0065

(0.0032)

* -0.0028

(0.0046) -0.0101

(0.0046) -0.0145

(0.0045) -0.0132

(0.0044) -0.0150

(0.0066) -0.0141

(0.0064)

+0.0351

(0.0044) +0.0340

(0.0043) +0.0292

(0.0073) +0.0354

(0.0057)

0.04457

-3.48

(2.44) -7.88

(4.78) *-2.69

(3.05)

-2.97

(1.05) -4.35

(1.38) -2.46

(1.63)

+0.149

(0.084) +0.155

(0.084) * -0.265

(0.863)

+0.0422

(0.0312) +0.1266

(0.0506)

* +0.0093

(0.0414)

0.04305

0.04076

0.04391

+0.0532

(0.0063) +0.0505

(0.0062) +0.0411

(0.0104) +0.0547

(0.0083)

0.04456

-3.08

(2.43)

* -4.33

(4.73) *-3.07

(3.09)

-2.88

(1.06) -3.96

(1.43) -2.61

(1.66)

+0.124

(0.085) +0.124

(0.087)

* -0.324

(0.872)

+0.0361

(0.0314) +0.1172

(0.0524)

* -0.0090

(0.0419)

0.04336

0.04219

0.04450

Table 13-45. Frequency distribution of cements with respect to AE 98/70, the ratio of dynamic modulus of Series A concretes determined after i. weeks in water divided by the values after the previous 8 weeks in laboratory air

Dynamic E ratio

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 Type cement to to to to to to to to to Total

1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45

Number of cements

I 16

1 10

34

321

2

7

15

18

2

16

10

214

1 79

867

320

315

lA

II 4

1 2 IIA

III 8 4

2

1 IILA. IV, V 5 2 2 1

Total ... 8 33 73 42 28 6 4 0 1 195

101
Table 13-46. Coefficients for equations relating AE 98/70, the ratio of dynamic You

(after drying in air) of Series A concretes made with

Note Const. Air

content CaA CaS CiAF CaO AE 98/70

s.d. AE 98/70

s.d. AE 98/70

s.d. AE 98/70

s.d. AE 98/70 (odd)

s.d. AE 98/70 (even)

s.d. AE 98/70

s.d. AE 98/70

s.d. AE 98/70 (odd)

s.d. AE 98/70 (even)

s.d.

= +1.447

= (0.040)

= +1.332

: (0.059) +1.315

^ (0.040) +1.333

(0.039)

: +1.299

= (0.056)

= +1.390

' (0.056)

= +1.795

= (0.291)

= +1.918

= (0.285)

= +1.595

= (0.468)

= +2.022

= (0.368)

+0.00455

(0.00158) +0.00469

(0.00155) +0.00469

(0.00155) +0.00491

(0.00151) +0.00566

(0.00193) +0.00424

(0.00256) +0.00446

(0.00152) +0.00452

(0.00148) +0.00499

(0.00192) +0.00427

(0.00251)

+0.00458

(0.00134) -0.01209

(0.00656) -0.01446

(0.00228) -0.01555

(0.00224) -0.01831

(0.00356) -0.01550

(0.00294)

-0.00308

(0.00051) -0.00351

(0.00053) -0.00358

(0.00050) -0.00376

(0.00049) -0.00299

(0.00070) -0.00471

(0.00072)

+0.00334

(0.00177) +0.00313

(0.00174) +0.00308

(0.00173) +0.00325

(0.00169) +0.00322

(0.00252)

* +0.00229

(0.00237) -0.0187

(0.0040) -0.0211

(0.0039) -0.0163

(0.0062) -0.0238

(0.0052)

Note 1, 172 cements, Avg. = 1.148, S.D. = 0.06000 Note 2, 86 cements

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

Table 13-47. Coefficients for equations relating AE 98/70, the ratio of dynamic You

(after drying in air) of Series A concretes made

Note Const.

Air content AE 98/70

s.d. = +1.435 = (0.042) +0.00674

(0.00385) AE 98/70

s.d. = +1.332 = (0.061) +0.00698

(0.00380) AE 98/70

s.d. = +1.304 = (0.041) +0.00700

(0.00380) AE 98/70

s.d. = +1.322 = (0.040) +0.00854

(0.00386) AE 98/70 (odd)

s.d. = +1.282 = (0.059)

* +0.00532

(0.00657) AE 98/70 (even)

s.d. = +1.355 = (0.058) +0.01100

(0.00495) AE 98/70

s.d. = +1.891 = (0.297) +0.00609

(0.00373) AE 98/70

s.d. = +2.010 = (0.290) +0.00751

(0.00379) AE 98/70 (odd)

s.d. = +2.103 = (0.483)

* +0.00297

(0.00654) AE 98/70 (even)

s.d. = +1.964 = (0.366) +0.01103

(0.00479)

CsA

+0.00493

(0.00138) -0.00309(0.00053) +0.00375

(0.00180) -0.01019

(0.00673) -0.00346

(0.00055) +0.00352(0.00178) -0.01411

(0.00237) -0.00357(0.00052) +0.00343(0.00177) -0.01528

(0.00232) -0.00376

(0.00051) +0.00358(0.00173) -0.01652

(0.00364) -0.00367(0.00072) +0.00597(0.00288) -0.01431

(0.00317) -0.00408(0.00076) +0.00244(0.00225)

C4AF CaO

-0.0199

(0.0040) -0.0223

(0.0040) -0.0237

(0.0064) -0.0219

(0.0051)

Note 1, 161 cements, Avg. = 1.148, S.D. = 0.05965 Note 2, 81 cements Note 3, 80 cements

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

102
ng's modulus of elasticity at 98 days (after 28 days soaking in water) to that at 70 days

AE + NAE cements, to various independent variables

S03 K2O Loss C3ASO3 AhOsSO3 MgO Li P Co S.D.

-0.0856

(0.0106)

* -0.0117

(0.0303)

-0.0519

(0.0168) -0.0527

(0.0165) -0.0532

(0.0164) -0.0632

(0.0164) -0.0611

(0.0241) -0.0590

(0.0241) -0.0565

(0.0168) -0.0698

(0.0169) -0.0754

(0.0242) -0.0651

(0.0251)

-0.0158

(0.0062) -0.0181

(0.0062) -0.0187

(0.0060) -0.0172

(0.0059) -0.0160

(0.0087) -0.0181

(0.0087) -0.0217

(0.0068) -0.0215

(0.0067) -0.0157

(0.0107) -0.0225

(0.0093)

-0.00929

(0.00290) -0.00858

(0.00286) -0.00850

(0.00285) -0.00716

(0.00281) -0.00448

(0.00409) -0.01158

(0.00428) -0.01314

(0.00394) -0.01288

(0.00384) -0.00729

(0.00648) -0.01699

(0.00517)

0.04053

+0.0313

(0.0120) +0.0357

(0.0041) +0.0356

(0.0040) +0.0384

(0.0062) +0.0372

(0.0054)

0.03983

0.03973

-2.19

(0.91) -2.74

(1.47) -1.62

(1.22)

+0.0667

(0.0291) +0.1949

(0.0591)

* +0.0317

(0.0341)

-3.22

(2.13) -6.43

(3.31) *+0.22

(2.95)

0.03861

0.03887

0.03792

+0.0566

(0.0058) +0.0551

(0.0056) +0.0547

(0.0088) +0.0600

(0.0076)

0.03965

-2.28

(0.91) -2.92

(1.49) -1.74

(1.20)

+0.0605

(0.0289) +0.1741

(0.0597)

* +0.0322

(0.0337)

-3.28

(2.10) -5.15

(3.23) *-0.31

(2.94)

0.03853

0.03936

0.03786

ng's modulus of elasticity at 98 days {after 28 days soaking in water) to that at 70 days

with NAE cements, to various independent variables

K20 Loss

-0.0533

(0.0175) -0.0127(0.0064) -0.0535

(0.0173) -0.0151(0.0064) -0.0543

(0.0172) -0.0162(0.0062) -0.0665

(0.0174) -0.0142(0.0061) -0.0536

(0.0270) -0.0190

(0.0111) -0.0760

(0.0242) -0.0137

(0.0078) -0.0589

(0.0175) -0.0200

(0.0070) -0.0745

(0.0177) -0.0191(0.0068) -0.0703

(0.0277) -0.0226(0.0131) -0.0802

(0.0243) -0.0180(0.0082)

C3A

S03

A1203 S03 MgO Li Co

+0.0282

(0.0123) +0.0354

(0.0042) +0.0354

(0.0041) +0.0394

(0.0064) +0.0339

(0.0056) +0.0564

(0.0059) +0.0551

(0.0057) +0.0591

(0.0091) +0.0570

(0.0078)

-0.00939

(0.00296) -0.00876

(0.00294) -0.00863

(0.00292) -0.00699

- (0.00290)

* -0.00420

(0.00440) -0.00870

(0.00421) -0.01428

(0.00405) -0.01371

(0.00394) -0.01249

(0.00649) -0.01427

(0.00511)

-2.46

(0.95) -2.21

(1.60) -2.93

(1.28)

-2.52

(0.94) -2.33

(1.60) -3.09

(1.23)

+0.0604

(0.0295) +0.1687

(0.0504)

! -0.0046

(0.0380)

+0.0552

(0.0292) +0.1667

(0.0510)

* -0.0106

(0.0363)

-3.39

(2.20)

*1.92

(2.87) -6.89

(3.76)

-3.48

(2.16) *-1.43

(2.83) -7.92

(3.64)

103
Table 13-48. Calculated contributions of independent vari- ables to AE 98/70, the ratio of the dynamic modulus of

Series A concretes after 28 days in water divided by the dynamic modulus after the previous 8 weeks in air

^sicuiateci

T J inde- Ivange oi Ooefiicierits Oalculateu range of pendent variables from eq 4 contributions contribuvariable (percent) la Die Lo—'it to AEjyo/ i\j tions to

Prtnof — -1-1 ^99

Air-content, cements. 0 to 4.0 _i_n nnoKA U CO T^U.UOO 0.038 CjA 1 to 15 -0.01528 -0.015 to -0.229 o!214 C3S 20 to 65 -0.00376 -0.075 to -0.244 0.169 CAF 1 to 17 +0.00358 +0.004 to +0.061 0.057 K2O 0 to 1.1 -0.0665 0 to -0.073 0.073 Loss - 0.3 to 3.3 -0.0142 -0.004 to -0.047 0.043 C3A/SO3- - 0.4 to 10.1 +0.0354 +0.014 to +0.358 0.344 MgO 0 to 5.0 -0.00699 -0.007 to -0.035 0.028

Li 0 to 0.02 -2.46 0 to -0.049 0.049 P 0 to 0.5 +0.0604 0 to +0.030 0.030 Co** 0 to 0.01 -3.39 0 to -0.033 0.033

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

Table 13-49. Frequency distribution of cements with respect

to OE 71 1 70, the ratio of dynamic modulus of Series 0

concretes determined after 21 hours in water divided by the values after the previous 8 weeks in laboratory air

Dynamic B ratio

Type 0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 cement to to to to to to to to Total

0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08

Number of cements

I_ 1 7 18

118

24

3

17

16

2

19

12

10

13

2

76

864

320

313

IA 1 II 2 5 IIA

III 4 7

1

1

724 IIIA

IV, V 1 4 1 2

Total. 1 14 46 57 44 17 7 1 187

air-dried Series A concretes (AE71/70) is pre- sented in table 13-53. As was found for the Series

0 concretes, the Series A concretes made with

most of the cements showed a slight reduction of dynamic modulus when the air-dried specimens were placed in water for 24 hours. There was an

overlapping of the values for the concretes made

with the different types of cement.

Equations are presented in table 13-54 indicating the independent variables associated with

the AE71/70 dynamic-modulus ratio of concretes made v/ith AE -|- NAE cements. The use of the

commonly determined independent variables, air content, C3A, C3S, K2O, C3A/SO3 and MgO in eq 1 resulted in a highly significant reduction of the S.D. value. The additional use of the trace elements Zr, Co, Li, Rb, and Ni as independent

variables in eq 2 resulted in a further significant

reduction of variance. In eq 4 the use of the trace elements Zr, Co, Li, Rb, Ni, and Ti, together with

the commonly determined variables, also resulted

*in a significant reduction of variance. (See table

13-57.)

In eqs 2A, 2B, 4A, and 4B calculated for the

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

coef./s.d. ratios for C3S, Loss, MgO, Zr, Rb, Ni,

and Ti were less than 1.0 in one or more of the

equations for the smaller lots of cement.

A corresponding series of equations for the NAE

cements is presented in table 13-55. The independent variables, their coefficients, and coef./s.d.

ratios were generally in agreement with those of the previous table where the AE cements were

included. The use of commonly determined independent variables or these with the trace elements

resulted in a significant reduction of variance.

Using the coefficients of the independent variables of eq 2 table 13-55 and the ranges of these

variables, computations were made of the esti- mated contributions to the AE71/70 dynamicmodulus values. These calculated contributions

are presented in table 13-56 together with the

calculated ranges of these contributions. Higher

values for air content and C3A/SO3 were associated with higher ratios (AE71/70).

Higher values for C3A, K2O, and possibly Loss,

MgO, and Li were associated with lower values

for the ratio.

104
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105
Table 13-52. Calculated contributions of independent variables

to OE 71/70, the ratio of dynamic modulus of Series O

concretes after 2U hours in water divided by the dynamic

modulus after the previous 8 weeks in air

Inde- pendent

variable

Range of variables

(percent)

Coefficients from eq 2

table 13-51

Calculated

contributions

to OE71/70

(calculated range of contributions to OE71/70

Const. = +1.045

Air-content, NAE

cements. 0 to 4.5 +0.00634 0 to +0.029 0.029 C3A 1 to 15 -0.00395 -0.004 to -0.059 0.055 C3S** OA to DO —0 00049 —0 OOS tn 0 097 0.019 K2O 0 to 1.1 -0.020 0 to -0.022 0]022 C3A/SO3.- 0.4 to 10.1 +0.00646 +0.003 to +0.065 0.062 Loss 0.3 to 3.3 -0.0156 -0.005 to -0.051 0.046 MgO 0 to 5.0 -0.00284 0 to -0.014 0.014 Co** 0 to 0.01 -1.63 0 to -0.016 0.016 Ni 0 to 0.02 -1.12 0 to -0.022 0.022 Zr 0 to 0.5 +0.128 0 to +0.064 0.064 Mn** 0 to 1.0 -0.0152 0 to -0.015 0.015

Table 13-53. Frequency distribution of cements with respect

to AE71/70, the ratio of dynamic modulus of Series A

concretes determined after 2^ hours in water divided by the values after the previous 8 weeks in laboratory air

Dynamic E ratio

0.94 0.96 0.98 1.00 1.02 1.04 Type cement to to to to to to Total

0.96 0.98 1.00 1.02 1.04 1.06

Number of cements

I.. 6 23 24 12 9 74 ia 2 4 2 8

II 2 18 15 19 5 4 63 iia 1 1 1 3 in 3 9 5 3 20 IIIA 2 1 3

IV, V 1 5 4 1 2 13

Total 11 51 54 44 18 6 184

**Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0.

Table 13-54. Coefficients for equations relating AE 71/70, the ratio of dynamic Yo

days (after drying in air) of Series A concretes made

Eq. No. Note Const.

Air content CaA CsS SiOj K2O Loss

1-.

2..

2A

2B

3-.

4..

4A

4B

AE 71/70

s.d. AE 71/70

s.d. AE 71/70 (odd)

s.d. AE 71/70 (even)

s.d. AE 71/70

s.d. AE 71/70

s.d. AE 71/70 (odd)

s.d. AE 71/70 (even)

s.d.

= +1.030

= (0.012)

= +1.038

= (0.012) +1.038

(0.018)

: +1.035

(0.020) +0.841

(0.039) +0.842

(0.038)

: +0.882

(0.052)

^ +0.797

: (0.060)

+0.00379

(0.00071) +0.00399

(0.00068) +0.00377

(0.00116) +0.00434

(0.00097) +0.00364

(0.00070) +0.00393

(0.00068) +0.00370

(0.00115) +0.00422

(0.00096)

-0.00428 -0.000394

(0.00103) (0.000223) -0.00454 -0.000382

(0.00099) (0.000216) -0.00296 -0.000446

(0.00155) (0.000280) -0.00537 * -0.000263

(0.00141) (0.000385) +0.00612

(0.00145) +0.00657

(0.00141) +0.00485

(0.00189) +0.00833

(0.00228)

-0.0205

(0.0077) -0.0295

(0.0086) -0.0245

(0.0118) -0.0370

(0.0148) -0.0185

(0.0076) -0.0288

(0.0085) -0.0256

(0.0113) -0.0307

(0.0149)

-0.00906

(0.00281) -0.00882

(0.00279) -0.01102

(0.00382) -0.00656

(0.00467) -0.00652

(0.00299) -0.00682

(0.00299) -0.00994

(0.00411)

* -0.00243

(0.00492)

Note 1, 163 cements, Avg. = 0.9909, S.D. = 0.02300 Note 2, 82 cements Note 3, 81 cements

*Coef./s.d. ratio less than one. Table 13-55. Coefficients for equations relating AE 71/70, the ratio of dynamic Youn

days (after drying in air) of Series A concretes made

Eq. No. Note Const. Air content CsA C3S Si02 K2O Loss

1..

2..

2A

2B

3..

4..

4A,

4B

AE 71/70

s.d. AE 71/70

s.d. AE 71/70 (odd)

s.d. AE 71/70 (even)

s.d. AE 71/70

s.d. AE 71/70

s.d. AE 71/70 (odd)

s.d. AE 71/70 (even)

s.d.

+1.026

(0.013) +0

(0 +1.035

(0.013) +0

(0 +1.044

(0.019) +0

(0 +1.027

(0.021) +0

(0 +0.844

(0.041) +0(0 +0.841

(0.040) +0(0 +0.822

(0.062) +0

(0 +0.851

(0.056) +0(0.

-0.00435 -0.000352

(0.00109) (0.000237) -0.00468 -0.000358

(0.00104) (0.000227) -0.00558 -0.000451

(0.00176) (0.000339) -0.00433 * -0.000341

(0.00146) (0.000354) +0.00592

(0.00153) +0.00649

(0.00148) +0.00766

(0.00224) +0.00566

(0.00212)

-0.0206

(0.0083) -0.0305

(0.0091) -0.0277

(0.0137) -0.0372

(0.0139) -0.0195

(0.0081) -0.0311

(0.0090) -0.0317

(0.0130) -0.0353

(0.0140)

-0.00856

(0.00298) -0.00790

(0.00294) -0.01046

(0.00474) -0.00459

(0.00427) -0.00604

(0.00316) -0.00599

(0.00314) -0.01016

(0.00494)

" -0.00226

(0.00458)

Note 1, 152 cements, Avg. = O.i *Coef./s.d. ratio less than 1.

9, S.D. = 0.2291 Note 1, 76 cements

106
Table 13-56. Calculated contributions of independent vari- ables to AE 71/70, the ratio of the dynamic modulus of

Series A concretes after 2^. hours in vjater divided by the dynamic modulus after the previous 3 weeks in air

Inde- pendent

variable

Range of variables

(percent)

Coefficients from eq 2 table 13-55

Calculated

contributions

to AE71/70

Calculated range of contributions to AE71/70

Const. = +1.035

Aircontent, NAE

cements- 0 to 4.5 +0.00635 0 to +0.029 0.029 C3A 1 to 15 —0.00468 —0.005 to —0.070 0.065 C3S** 20 to 65 -0.000358 -0.007 to -0.023 0.016 K2O 0 to 1.1 —nu.uouo n^oPi A trt n C\'iA yt Lfj —u.uoft Loss 0.3 to 3.3 -0.0079 -0.002 to -0.026 0.024 CaA/SOu. - 0.4 to 10.1 +0.0081 +0.003 to +0.082 0.079 MgO 0 to 5.0 -0.00307 0 to -0.015 0.015 Zr** 0 to 0.5 +0.0567 0 to +0.028 0.028 Co** 0 to 0.01 -1.82 0 to -0.018 0.018

Li 0 to 0.02 -0.912 0 to -0.018 0.018 Rb** 0 to 0.01 +1.68 0 to +0.017 0.017 Ni 0 to 0.02 -1.08 0 to -0.022 0.022

Coefficient of doubtful significance as coef./s.d. ratio was less than 2.0. ung's modulus of elasticity at 71 days (after soaking in water for 2^ hours) to that at 70

of AE + NAE cements, to various independent variables

CsA

"SO3

AI2O3 SOa MgO Zr Co Li Rb Ni Ti S.D.

+0.00855

(0.00190) +0.00811

(0.00182) +0.00496

(0.00302) +0.00986

(0.00248)

-0.00388

(0.00135) -0.00328

(0.00134) -0.00261

(0.00206) -0.00382

(0.00206) -0.00234

(0.00137) -0.00191

(0.00137)

* -0.00115

(0.00212) -0.00237

(0.00207)

0.01837

+0.0580

(0.0341) +0.2239

(0.0887)

* +0.0217

(0.0404)

-1.85

(1.01) -1.81

(1.36) -1.91

(1.61)

-0.743

(0.430) -0.780

(0.587) -0.663

(0.662)

+1.84

(0.87) +1.86

(1.08) *+1.69

(1.60)

-0.978

(0.453) -0.813

(0.606) -1.144

(0.769)

0.01739

0.01697

0.01842

+0.0114

(0.0027) +0.0108

(0.0026) +0.00840

(0.00431) +0.01319

(0.00357)

0.01823

+0.0656

(0.0343) +0.2418

(0.0904)

* +0.0251

(0.0400)

-1.65

(0.99) -1.86

(1.34) -1.78

(1.57)

-0.813

(0.426) -0.804

(0.588) -0.848

(0.662)

+1.88

(0.86) +2.09

(1.08) *+1.35

(1.56)

-0.788

(0.455)

* -0.527

(0.609) -1.137

(0.746)

-0.0190

(0.0122) * -0.0202

(0.0220) -0.0250

(0.0160)

0.01726

0.01686

0.01814

g's modulus of elasticity at 71 days {after soaking in water for 21^ hours) to that at 70

of NAE cements, to various independent variables

CaA

SOa

AI2O3 SOa MgO Zr Co Li Rb Ni Ti S.D.

+0.00851

(0.00199) +0.00810

(0.00189) +0.00964

(0.00329) +0.00779

(0.00263)

-0.00382

(0.00142) -0.00307

(0.00141) -0.00392

(0.00230) -0.00222

(0.00216) -0.00237

(0.00144) -0.00181

(0.00145) -0.00259

(0.00223)

* -0.00070

(0.00225)

0.01881

+0.0567

(0.0349) +0.0542

(0.0405)

* +0.1258

(0.4165)

-1.82

(1.07) -3.77

(2.51) *-1.15

(1.26)

-0.912

(0.455) -1.279

(0.706) -0.757

(0.668)

+1.68

(0.90) *+0.88

(1.29) +2.57

(1.49)

-1.08

(0.47) -0.72

(0.70) -1.43

(0.74)

0.01767

0.01898

0.01751

+0.0112

(0.0028) +0.0108

(0.0027) +0.0121

(0.0045) +0.0098

(0.0038)

0.01870

+0.0653

(0.0351) +0.0703

(0.0397)

* +0.1160

(0.4206)

-1.59

(1.05)

* -2.39

(2.40) *-1.10

(1.27)

-0.990

(0.453) -1.592

(0.684) -0.685

(0.666)

+1.72

(0.89) *+0.90

(1.21) +2.55

(1.51)

-0.87

(0.47)

* -0.43

(0.68) -1.46

(0.74)

-0.0222

(0.0131) -0.0426

(0.0172)

* -0.0081

(0.0230)

0.01757

0.01826

0.01756

107
Table 13-57. "F" values for significance of reduction of variance due to added variables

Table Equation* "F"

ratio D.F.**

Critical "

= 0 01

F" Ratio

r» A (\K. CX, —

13-2 0,1 62.1 9:171 2.52 1.93

1,2 4.03 3:168 3.88 2.67

0 3 55.8 lO'lTO 2 40 1 89

3)4 4!o 3:167 3!88 2!67 13-3 0,1 26.5 8:160 2.62 2.00

1,2 2.61 4:156 3.44 2.42

0,3 23.5 9:159 2.52 1.93

3,4 2.60 4:155 3.43 2.42 13—6 0 1 25.1 2 :171 4.72 3 05

o!2 91.0 2^171 4!72 3!05

0,3 17.4 3:170 3.88 2.67

3,4 35.3 6:164 2.92 2.15

4,5 3.27 2:162 4.74 3.05 0 6 32 3 10:163 2 40

6!7 2.h0 3:160 3!89 2.67 13-7 0,4 20.8 9:153 2.52 1.93 4,5 2.66 3:150 3.90 2.67 0 6 18.7 10:152 2 40 1 89

6!7 2!71 3:149 3!90 2^67 13-10 0,1 60.9 9:170 2.52 1.93

1,2 3.89 1:169 6.77 3.90 0 3 63.3 9 '170 2 52 1 93

3)4 3^34 1:169 6^77 3!90 13-11 0,1 32.1 9:158 2.52 1.93

1,2 3.54 1:157 6.78 3.90

0,3 33.2 9:158 2.52 1.93 3,4 3.20 1:157 6.78 3.90 13—14 0 1 12.3 2:171 4 72 O.UO

o!2 4!51 2:171 4^72 3.05

0,3 8.60 3:170 3.88 2.67

3,4 27.8 7:163 2.75 2.07

4,5 2.72 3:160 3.89 2.67

0 6 29.0 9:164 2 52 1 93

6^7 3!45 2:162 4!73 3!05 13-15 0,4 18.9 10:152 2.40 1.89

4,5 2.96 3:149 3.90 2.67

0 6 21 9 9 "153 2 52 1.93

6)7 3.49 2!l51 4^75 3!05 13-18 0,1 63.9 10:169 2.40 1.89

1,2 1.38 1:168 6.76 3.90 0 3 69.9 9'170 2 52 1 93

Z,i 1.38 1:169 6.76 3!90 13-19 0,1 37.5 10:157 2.40 1.89

1,2 1.35 1:156 6.78 3.90

0,3 40.9 9:158 2.52 1.93

3,4 1.35 1:157 6.78 3.90 13-22 0 1 14 8 2 '171 A 79 3 05

0)2 6!l0 2:171 4.72 3!o5

0,3 10.1 3:170 3.88 2.67

3,4 43.5 8:162 2.62 2.00

4,5 2.40 1:161 6.77 3.90

0 6 35 4 10*163 2 40 1 89

6)7 2!23 1:162 6!77 3!90 13-23 0,4 24.5 11:151 2.38 1.87

4,5 3.96 1:150 6.78 3.90 0 6 26 7 2.40 1 89

6!7 3!47 1:151 6.78 3!90 13-26 0,1 91.1 8:171 2.62 2.00

1,2 6.09 3:168 3.88 2.67 80 6 9 :170 0 t;o 3,4 6!45 3:167 3.88 2.67 13-27 0,1 21.5 8:159 2.62 2.00

1,2 6.40 3:156 3.89 2.67

0,3 19.1 9:158 2.52 1.93

3 4 i .\jo 3:155 3.89 2.67 13-30 0,1 74.5 3:170 3.88 2.67

1,2 12.5 5:165 3.13 2.28

2,3 4.72 5:160 3.13 2.28

0,4 40.2 9:164 2.52 1.93

4,6 4.47 4:160 3.43 2.42 13-31 0,1 22.8 3:159 3.89 2.67

1,2 12.6 5:154 3.14 2.28

2,3 4.91 5:149 3.14 2.28

0,4 17.3 9:153 2.52 1.93

4,5 4.55 4:149 3.44 2.42

108

Table 13-57. "F" values for significance of reduction of variance due to added variables—Continued

Table Equation* "F"

ratio D.F.**

Critical *

a = 0.01

'F" Ratio

a = 0.05

13-34 0,1 22.5 7:172 2.75 2.07

1,2 3.38 3:169 3.88 2.67

0,3 19.4 8 169 2.62 2.00

3,4 3.76 3:168 3.88 2.67 13-35 0,1 20.8 8 159 2 62 2.00

1,2 2.72 3 156 3.89 2.67

0,3 20.9 8 159 2.62 2.00

3,4 3.12 3 156 3.89 2.67 13-38 0,1 18.8 8 163 2.62 2.00

1,2 3.23 3 160 3.88 2.67

0,3 18.6 8 163 2.62 2.00

3,5 3.51 3 160 3.88 2^67 13-39 0,1 18.0 9:151 2.53 1.93

1,2 2.30 3:148 3.90 2.67

0,3 17.8 9:151 2.53 1.93 13-42 0,1 26.2 9:170 2.52 1.93

1,2 3.70 4:166 3.43 2!42

0,3 29.0 8:171 2.62 2.00

3,4 3.10 4:167 3.43 2.42 13-43 0,1 23.7 9:158 2.52 1.93

1,2 3.84 4:154 3.44 2.42

0,3 26.5 8 159 2^62 2.00

3,4 3.23 4:155 3.44 2.42 13-46 0,1 23.8 9:163 2.52 1.93

1,2 6.78 1:162 6.77 3.90

0,3 25.5 9:163 2.52 1.93

3,4 4.20 3:160 3.88 2.67

0,5 28.7 8:164 2.62 2.00

5,6 4.22 3:161 3.88 2.67 13-47 0,1 21.8 9:152 2.53 1.93

1,2 5.21 1:151 6.78 3!90

0,3 23.2 9:152 2.53 1.93

3,4 4.25 3 149 3.90 2!67

0,5 26.5 8 153 2.62 2.00

5,6 4.38 3 150 3.90 2.67 13-50 0,1 14.0 8 161 2.62 2.00

1,2 7.0 4 157 3.43 2.42

0,3 19.6 6 163 2.92 2.15

3,4 6.55 4 159 3.43 2.42 13-51 0,1 11.6 8 149 2.62 2.00

1,2 6.74 4 145 3.44 2.42

0,3 15.8 6 151 2.92 2.15

3,4 6.26 4 147 3.44 2.42 13-54 0,1 12.6 8 155 2.62 2.00

1,2 4.59 5 150 3.14 2.28

0,3 14.8 7: 156 2.75 2.07

3,4 4.00 6: 150 2.92 2.15 13-55 0,1 10.2 8: 144 2.62 2.00

1,2 4.84 5: 139 3.15 2.28

0,3 11.9 7:145 2.76 2.07

3,4 4.21 6:139 2.93 2.15

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

fitted equation. **D.F. = degrees of freedom. Numbers preceding and following the

colon refer to degrees of freedom for the numerator and denominator of the "F" ratio, respectively.
7. Discussion

7.1. Independent Variables Associated with the

Dynamic Modulus of Elasticity

One equation selected from each of the tables

of equations representing Series 0 concretes made

of AE + NAE cements is presented in table 13-58,

columns 1, 2, 3, and 4, to facilitate a comparison

of the independent variables associated with the

dynamic modulus at the different ages and test conditions. The ratios of the dynamic modulus

values at the different ages and curing conditions

are presented in columns 5, 6, and 7 of this table. The coef./s.d. values of the independent variables

and the calculated ranges of contributions to the

dynamic modulus and the ratios are also presented

in this table. Higher air contents were associated with lower

dynamic modulus values at all ages and conditions

(columns 1, 2, 3, and 4). Higher air contents were

associated with higher values of both the ratios

involving soaking, but there was no evidence of a

relationship with the OE70/14 ratio involving

drying. It was previously noted in part 3 section

7 table 7-77 that an increase in the air content was associated with a decrease of compressive

strength at all ages [18]. The coefficient for C3A was significant and

negative after the 56-day drying period (col 3)

and after the 28 days in water (col 4) as well as

for the three ratios (cols 5, 6, and 7). It was noted

in section 7 that C3A was associated with lower

compressive strengths at the later ages [18]. The coefficient for C3S was positive and highly

significant at each of the test conditions. This was

also true with respect to the compressive strength

of mortar cubes at early ages in section 7 [18]. In

column 6, the coefficient for C3S was negative and

highly significant.

The coefficient for C4AF was negative and significant at each of the test conditions (cols 1, 2,

8, and 4). No evidence was found for a strong

correlation with the compressive strength in sec- tion 7 [18]. The coefficient for SO3 was positive and highly

significant at each of the test conditions (cols 1, 2, 3, and 4) and also for the OE70/14 ratio (col 5). The coefficient for C3A/SO3 was positive and

highly significant for the OE98/70 and OE71/70

ratios. The SO3 was also positive in the equations

for 1, 3, and possibly 7-day compressive strength

of 1:2.75 (cement to sand) mortar cubes in sec- tion 7 [18] and also for the equation for the cubes

stored in air. The coefficient for Na20 was positive and significant at 14 days in the dynamic tests (col 1). This differs from the results of static strength

tests (See part 4, section 7) where there was no

evidence of a relationship at the early ages, but

at 1, 5, and 10 years the coefficient had a negative

sign. The coefficients for K2O were not highly

significant in the dynamic tests but were probably significant at early ages in the compressive

strength tests [18]. An increase in fineness was associated with a

decrease in dynamic modulus after 28 and 56 days

drying and 28 days resoaking. As previously

indicated in part 3 section 7, an increase in fineness was associated with an increase of compressive

strength of mortar cubes [18]. The coefficient for loss-on-ignition was positive

in the equation for the dynamic modulus after 8

weeks of drying (col 3) and was also significant

but with a negative sign in cols 5, 6, and 7 with

the ratios for the different conditions. Higher

loss-on-ignition was associated with lower compressive strength of mortar cubes at the early

ages [18]. In general the coefficients for the trace elements were not highly significant. Of the 19 included in table 13-58, 8 had coef./s.d. ratios of 2.0 or

greater, and one of these (Zr in col. 7) was greater

than 3.0. Equations for the Series A concretes made with

a slump of 5 + 1-in are presented in table 13-59.

An increase of the amount of water required to obtain the desired slump was associated with lower

dynamic-modulus values at each of the test conditions. It has previously been indicated in part 1, section 2 [16] that the water/cement ratio is also a function of the properties of the cements. Thus,

interaction of this variable with other so-called

independent variables of the equations is a possibility. In general, the differences in air content,

w/c, C3S, and SO3 of the cements of the Series A

concretes had the greatest effect on the calculated

ranges of contributions after 14 days moist curing

and after both 4 and 8 weeks of drying (cols 1, 2, and 3), and an increase of C3A was associated

with lower strengths after the 28 days in water

(col 4).

7.2. Effect of Trace Elements

Evidence from many of the previous tables in

this section, especially those dealing with the wet

specimens, shows that the additional use of the

trace elements in an equation generally caused a

significant reduction in variance. After 4 or 8

weeks drying there was no evidence that the trace elements had a significant effect. (See tables

13-10, 13-11, 13-14, 13-15, 13-18, 13-19, 13-22,

13-23, and 13-57.) In equations for the ratios,

inclusion of the trace elements resulted in a more

significant reduction of variance for the AE71/70

and OE71/70 ratios, and somewhat less for the

98/70-day ratio. There were more instances of questionable significance for the 70/14-day ratios

of dynamic modulus values.

109
Table 13-58. Coefficients, coef./s.d. ratios, and calculated ranges of contributions of independent variables associated with the dynamic modulus values of Series 0 concretes at various ages

Column 1 2 3 4 5 6 7 Eq. No. 2 2 2 2 2 2 2 Table No. 13-2 13-10 13-18 13-26 13-34 13-42 13-50 Dependent variable Constant

0D14

+3.723

OD42

+3.665

OD70

+3.523

OD98

+5.25

OE70/14

+0.880

OE98/70

+1.374

OE71/70

+1.046

Air content, coef -0.1598

20.7

1.59 +0.01007

1.7 0.14 +0.0196

9.3 0.88 -0.0178

2.4 0.25 +0.160

3.9 0.32

-0.1549

19.9

1.55 -0.0086

1.5 0.12 +0.0168

7.3 0.76 -0.0224

2.9 0.31 +0.507

10.3 1.01

-0.1567

19.8

1.57 -0.0256

4.1 0.36 +0.0181

7.9 0.81 -0.0302

8.9 0.42 +0.551

7.9 1.10

-0.1400

26.9

1.40 -0.0152

3.7 0.21 +0.00601

3.9 0.27 -0.0142

2.7 0.20 +0.183

5.4 0.37

+0.0101

5.3 0.101 -0.0178

7.4 0.249 -0.00411

7.8 0.185 +0.00261

1.4 0.036

+0.00435

5.3 0.044 -0.00412

4.1 0.058 -0.000418

1.8 0.018

Coet./s.d Calculated range -0.00587

6.9 0.082

Coef./s.d Calculated range

CsS, coef Coef./s.d Calculated range C4AF, coef... Coef./a.d. Calculated range

SO3, coef +0.0698

8.0 0.184

Coef./B.d Calculated range C3A/SO3, coef +0.0339

8.1 0.329

+0.00702

3.8 0.068

Coef./s.d

NajO, coef +0.260

3.2 0.18 +0.148

1.9 0.16 +0.0240

1.9 0.12

+0.210

2.5 0.15

-0.0385

2.6 0.027

Coef./s.d Calculated range K2O, coef -0.102

1.3 0.11 +0.0308

2.4 0.15 -0.000128

3.5 0.88 +0.116

4.1 0.35

-0.0495

2.8 0.054

-0.0213

2.8 0.023 -0.00215

1.6 0.011

Coef./s.d Calculated range MgO, coef +0.0246

2.0 0.12 -0.000099

3.0 0.30

+0.00225

1.1 0.011 -0.0000170

2.9 0.051 -0.0259

5.1 0.078

Coef./s.d Calculated range APF, coef -0.000078

3.8 0.23 -0.0361

1.9 0.11 -0.663

2.8 0.13

Coef./s.d

-0.0282

8.6 0.070

-0.0165

5.9 0.050

Coef./s.d.

Coef./a.d

-8.18

1.3 0.081

-2.07

2.0 0.021Coef./s.d

-3.284

2.0 0.16

-2.84

2.1 0.12 Coef./s.d

-2.58

2.6 0.051

Coef./s.d

Mn, coef -0.188

1.6 0.19

+0.0324

1.6 0.032

-0.0199

1.6 0.020 -0.898

2.0 0.018

Coef./8.d Calculated range

Ni, coef Coef./s.d

P, coef +0.0506

1.7 0.025

Coef./s.d Calculated range Rb, coef +18.63

2.4 0.19

-2.14

1.6 0.021

Coef./s.d Calculated range V, coef -1.019

1 9

0.10

P.nof /a H

Zr, coef. +0.561

1.7 0.28

+0.619

2.7 0.32

-0.134

2.1 0.067

+0.162

1.9 0.081

+0.130

8.6 0.065

Coef./B.d

110
Table 13-59. Coefficients, coef./s.d. ratios, and calculated ranges of contributions of independent variables associated with the dynamic modulus values of Series A concretes at various ages

Column 1 2 3 4 6 6 7 Eq. No. 5 6 5 3 2 4 2 Table No. 13-6 13-14 13-22 13-30 13-38 13-46 13-54 Dependent variable Constant

AD14

+7.870

AD42

+7.766

AD70

+6.621

AD98

+9.589

AE70/14

+0.905

AE98/70

+1.333

AE71/70

+1.038

-0.1406

12.7

1.83 -6.435

6.9 1.09

-0.1260

9.7 1.64 -6.649

5.9 1.13 -0.0102

1.5 0.14 +0.0173

6.7 0.78 -0.0193

2.9 0.27 +0.508

2.3

1.02

-0.1236

9.8

1.61 -5.356

4.9 0.91 -0.0336

4.9 0.47 +0.0183

7.3 0.82 -0.0299

3.6 0.42 +0.532

9.3 1.06

-0.1285

16.1

1.67 -6.795

9.8 1.16 -0.0179

4.2 0.25 +0.00475

3.1 0.21 -0.0166

3.2 0.23 +0.204

5.8 0.40

+0.00491

3.2 0.064

+0.00399

5.9 0.052

Coef./s.d Calculated range. : —

w/c, coef. Coef./s.d Calculated range

C3A, coef -0.00714

6.9 0.104

-0.01555

6.9 0.218 -0.00376

7.7 0.169 +0.00325

1.9 0.045

-0.00454

4.6 0.063 -0.000382

1.8 0.017

Coef./s.d Calculated range

C3S, coef +0.0190

9.0 0.86 -0.0273

4.3 0.38 +0.211

5.0 0.42

Coef./s.d Calculated range C4AF, coef -0.00173

1.3 0.024 +0.0722

8.0 0.144

Coef./s.d Calculated range

SO3, coef Coef./s.d Calculated range C3A/SO3, coef +0.0356

8.9 0.345

+0.00811

4.5 0.079

Coef./s.d

NajO, coef +0.270

3.4 0.19 +0.222

3.0 0.24 +0.0226

1.8 0.11

-0.0434

2.95 0.030

Coef./s.d Calculated range K2O, coef +0.249

3.0 0.27 +0.0349

2.6 0.17 -0.000088

2.3 0.26 +0.0951

3.1 0.28

-0.0632

3.9 0.070 -0.00716

2.5 0.036

-0.0295

3.4 0.32 -0.00328

2.4 0.016

Coef./s.d Calculated range +0.0348

2.5 0.17 -0.000104

2.7 0.31 +0.0452

1.4 0.14

+0.0037

1.8 0.019 -0.0000166

2.8 0.050 +0.0203

4.0 0.061

Coef./s.d Calculated range APF, coef -0.000051

2.3 0.15

Coef./3.d Calculated range -0.0172

2.9 0.052

-0.00882

3.2 0.026

Coef./s.d

-0.428

1.5 0.09 Coef./s.d

Co, coef +2.59

1.5 0.026

-3.22

1.5 0.032

-1.85

1.8 0.018

Coef./s.d

Cu, coef -4.41

2.3 0.22 +9.11

2.0 0.18

-3.02

2.7 0.15Coef./s.d Calculated range

Li, coef +7.07

1.6 0.14

-2.19

2.4 0.043

-0.743

1.7 0.014 -0.978

2.2 0.020

Coef./s.d Calculated range

Coef./s.d

Mn, coef -0.185

1.7 0.18

+0.0396

1.9 0.040 +0.0667

2.3 0.033 -2.45

1.8 0.024

Coef./s.d Calculated range

P, coef Coef./s.d

Rb, coef +14.86

1.9 0.15

+8.60

1.7 0.09 -0.165

0.16 +0.541

2.4 0.27

+1.84

2.1 0.018

Coef./s.d Calculated range

Ti, coef

Calculated range

Zr, coef +0.381

1.0 0.19

-0.0580

1.7 0.029

i

111
6.0

5.0

9 4.0 X

LU

>•o

3.0

aQ

2.0

1.0 2.0 4.0 6.0 8.0 10.0

I Day COMPRESSIVE STRENGTH, psi X lO^

Figure 13-1. Dynamic Young's modulus of elasticity at 1 day versus the 1-day compressive

strength of 1 :2.75 {cement to graded Ottawa sand) mortars.

7.3. Relationships of Dynamic Modulus to

Various Characteristics of Mortar Bars

Investigation was made of the relationship between 14-day dynamic modulus of the concretes and the following characteristics of 4- X 4- X 16-

cm mortar bars made with the same cements: (1) 7-day dynamic modulus of the bars, (2) modulus

of rupture of the bars, and (3) compressive

strengths of modified cubes from the ruptured

bars. In none of these cases was a significant

relationship found.

Relationships between dynamic modulus, compressive strength, and modulus of rupture of the

4- X 4- X 16-cm mortar prisms at 1, 3, and 7

days age are presented graphically in figures 13-1

through 13-9. The first three figures show rela- tionships between dynamic modulus and compressive strength at the three ages. Figures 13-4

through 13-6 show dynamic modulus versus modulus of rupture, and figures 13-7 through 13-9

show compressive strength versus modulus of rupture.

Highly significant relationships evidently exist

between these three variables when measured on

the same specimens. The relationships appear to be nonlinear, however.

7.4. Compressive and Flexural Tests

of Concretes

No compressive or flexural strengths of these concretes were determined at the time the cements

were tested. At the age of 7 years, 24 pairs of

3- X 4- X 16-in specimens were removed from the

field exposure and placed in water for 28 days.

Then resonant frequency and flexural and compressive strengths were determined on one of the

beams. The compressive strengths were determined on 3- X 3- X 4-in prisms sawed from the broken

beams. No correction was made for the nonstandard shape and height-width ratio of the

specimens. The specimens selected were all from

concretes which had the same w/c for the Series

0 and Series A concretes. The average dynamic modulus of elasticity was

5.58 X lO*' psi with a range of values from 4.95 to

5.96 X 10'^ psi. The average compressive strength was 4350 psi with a range of 3040 to 5660 psi The

average modulus of rupture was 624 psi with a range of 490 to 770 psi. The trends of the rela- tionships are indicated by the dashed lines in

figures 13-10 and 13-11. No trend line was placed

in figure 13-12 showing the relationship of compressive to flexural strengths because of the broad

112
2.0 4.0 6.0 8.0

3 Day COMPRESSIVE STRENGTH, psi X 10"'

10.0

Figure 13-2. Dynamic Young's modulus of elasticity at 3 days versus the 3-day compressive

strength of 1 :2.75 (cement to graded Ottawa sand) mortars.

scatter of results. The ranges of values of the

concretes selected for these tests were much less than those of the 1-, 3-, and 7-day mortar tests in Figures 13-1 through 13-9, and this makes it more difficult in the case of concretes to establish

overall trends.

7.5. Effect of Drying and Resoaking on Dynamic

Modulus of Concretes

The average dynamic-modulus values and aver- ages of the ratios for 70/14-, 98/70-, and 71/70-day

dynamic-modulus values have been presented in the tables of equations. There was an average

reduction of dynamic modulus of 7 percent when

the specimens were dried for 8 weeks, an average

increase of dynamic modulus of 15 percent when

the dried specimens were placed in water for 28

days. When the air-dried specimens were placed

in water for 24 hours the average dynamic modulus for all specimens was about 1 percent less than

when measurements were made on the dry

specimens.

However, consideration must be given to the

broad distribution of values for all of the ratios as

it was evident that concretes made of the different

cements behaved quite differently. Drying and

wetting can produce tensile and compressive

stresses in a concrete specimen and these may be

factors affecting the fundamental resonant fre- quencies of the specimens. Soaking the air-dried

specimens in water for 24 hours resulted in as much as 5-percent reduction in dynamic modulus

for some specimens and in others, up to a 5- percent increase in dynamic modulus. It has

previously been noted that the saturation ratio

(part 5 section 11) also varied with concretes made

of different cements. Whereas some specimens were about 80 percent saturated in 24 hours,

others were only about 20 percent saturated. The

slight reduction in dynamic modulus with 24

hours of resoaking of the air-dried specimens of some of the cements may have resulted from a

relief of possible tensile stresses on the skin of the

specimens whereas the slight increase may have

resulted from the filling of the voids.

One of the contributing factors to the 70/14-day

ratio was undoubtedly the continued hydration

which occurred during the 56-day storage in laboratory air. The rate of hydration may have been

different for concretes made with different ce- ments. The loss of different quantities of water

113
2.0 4.0 6.0 8.0

7 Day COMPRESSIVE STRENGTH, psi X 10"^

10.0

Figure 13-3. Dynamic Young's modulus of elasticity at 7 days versus the 7-day compressive

strength of 1:2.75 {cement to graded Ottawa sand) mortars.

as indicated in section 12 would result in differ- ences of the voids of the different concretes.

It was noted that the 98/70-day ratios were all greater than 1.0 but there was a broad distribution

of values. The extent of filling of the pore structure plus continued hydration could account for the

increase in dynamic modulus and for some of these differences.

When concrete specimens are exposed to out- door weathering, the dynamic modulus of elas- ticity may be affected by the moisture condition

and moisture distribution within the specimens.

Unless there are gross differences in dynamic

properties there would be the uncertainty of the

role of the moisture condition. If specimens are kept moist prior to measurement there is, as indicated in section 11, a possibility of autogenous

healing. Measurements made on the specimens

stored outdoors indicated a slight (perhaps significant) increase in dynamic modulus in the fall as compared to measurements made in the spring

after the winter freezing and thawing exposure.

Factors other than normal weathering may have

been responsible.

114
6.0

0.2 0.4 0.6 0.8

I Day MODULUS of RUPTURE, psi X 10''

Figure 13-4. Dynamic Young's modulus of elasticity at 1 day versus the 1-day modulus of rupture

of 1 :2.75 (cement to graded Ottawa sand) mortars.
0.2 0.4 0.6 0.8

3 Day MODULUS of RUPTURE, psi X 10"'

Figure 13-5. Dynamic Young's modulus of elasticity at 3 days versus the 3-day modulus of rupture of 1:2.75 {cement to graded Ottawa sand) mortars.
0.2 0.4 0.6 0.8

7 Day MODULUS of RUPTURE, psi X 10"'

Figure 13-6. Dynamic Young's modulus of elasticity at 7 days versus the 7-day modulus of rupture of 1:2.75 (cement to graded Ottawa sand) mortars.
10.0

-3

I Day MODULUS of RUPTURE, psi X 10

Figure 13-7. Compressive strength at 1 day versus the modulus of rupture at 1 day of 1:2.75 {cement to graded Ottawa sand) mortars.
10.0

0.2 0.4 0.6 0.8

3 Day MODULUS of RUPTURE, psi X lO'^

Figure 13-8. Compressive strength at 3 days versus the 3-day modulus of rupture of 1:2.75 {cement

to graded Ottawa sand) mortars.
10.0

8.0 —

10

IO

6.0 —

CLO 4.0 o

>«oa

2.0

0.2 0.4 0.6 0.8 1.0

7 Day MODULUS of RUPTURE, psi X 10"'

Figure 13-9. Compressive strength at 7 days versus the 7-day modulus of rupture of 1:2.75 (cement

to graded Ottawa sand) mortars.
COMPRESSIVE STRENGTH, psi X lO"

Figure 13-10. Dynamic Young's modulus of elasticity of concretes versus the compressive strength at 7 years after outdoor storage.
O S.4

60 6.S 7.0

MODULUS OF RUPTURE, psi X 10"^

Figure 13-11. Dynamic Young's modulus of elasticity of concretes versus the modulus of rupture at 7 years after outdoor exposure.
6.0

5.0

4.0

AVG. ® O

3.0

9.0 6.0 7.0 8j0

MODULUS of RUPTURE, psi X 10"*

Figure 13-12. Compressive strength of concretes versus the modulus of rupture

at 7 years after outdoor exposure.
8. Summary and Conclusions

(1) Measurements were made of the dynamic

Young's modulus of elasticity of concretes made

with 199 Portland cements from different mills. One series of concretes (Series 0) was made using a water/cement ratio of 0.635 and the other series (Series A) with the quantity of water adjusted to give a slump of 5 + 1 in. A nominal quantity of 5.5 bags of cement per cubic yard was used. The

3- X 4- X 16-in specimens were moist cured for 14 days, dried in laboratory air for 8 weeks, then

placed in water for 4 weeks. The fundamental

transverse frequency was determined at 14, 42,

70, 71, and 98 days. The ratios of the dynamic

modulus values at 70/14, 98/70, and 71/70 days were computed.

(2) The dynamic modulus after 14 days moist

curing ranged from 3.4 to 5.8 X lO*' psi, with an

average of 4.75 X 10'' psi for the Series 0 concretes amd 4.76 X 10'^ psi for the Series A concretes.

(3) After drying in laboratory air for 4 weeks

there was an average reduction of about 4 percent

in the dynamic modulus. There was, however, a broad distribution of values.

(4) After drying in laboratory air for 8 weeks

there was an average reduction of 7 percent in dynamic modulus. Concretes made with some of the cements showed an increase in dynamic modulus during the drying period, possibly due to continued hydration.

(5) When the concrete specimens which had

been air-dried for 8 weeks were placed in water

for 24 hours, the dynamic modulus of some decreased up to 5 percent and others increased up

to 5 percent.

(6) When the concrete specimens which had

been air-dried for 8 weeks were placed in water

for 4 weeks, there was an average of 15 percent

increase in dynamic modulus. There was a broad

distribution of values. Some concretes increased

only about 5 percent, and others had a 40-percent

increase in dynamic modulus.

(7) Computations of multivariable equations

by a least-squares method were used to investigate what chemical and physical properties of the

cements and concretes were associated with the

dynamic modulus of elasticity at the various ages, and with the ratios of the dynamic E at the

various ages after the different curing conditions.

The equations were computed for all the cements

for which minor constituents and trace elements

had been determined. The equations were computed using as independent variables, either the

major potential compounds, or the major oxides,

each with other commonly determined variables

and these with trace elements found to be significant.

The following observations relate to equations

as summarized in tables 13-58 and 13-59 for concretes made of AE -|- NAE cements using a

water/cement ratio of 0.635 and concretes having

a slump of 5 + 1 inches respectively

:

(7.1) An increase in the air content for both

series of concretes and the water/cement ratio

required to produce a concrete of the desired

slump for the Series A concretes was associated

with a decrease of the dynamic modulus at all conditions. An increase in the air content was

associated with an increase of the OE98/70 (28-

day soaking) and OE71/70-day (1-day soaking)

ratios of dynamic modulus for both series. (7.2) An increase of C3A was associated with a

decrease of the dynamic modulus after the 8-week

drying period and after the subsequent 4 weeks

in water. An increase in C3A was also associated

with a decrease of the dynamic modulus ratios,

70/14-day, 98/70-day, and 71/70-day.

(7.3) An increase of C3S was associated with an

increase of the dynamic modulus at all conditions

and with a decrease of the 98/70-day ratio.

(7.4) An increase of C4AF was generally asso- ciated with a decrease of the dynamic modulus at

all conditions although there were a number of instances where the coef./s.d. ratio was less than

3.0.(7.5) An increase of SO3 was associated with an

increase of the dynamic modulus at all conditions

and with the 70/14-day ratio. An increase of C3A/SO3 was associated with an increase of the

98/70-day and 71/70-day ratios of dynamic modulus. The C3A/SO3 ratio interacts with the coeffi- cients for C3A and SO3 and all must be taken into

consideration in evaluating the effect. (7.6) An increase in Na20 was associated with an increase of the dynamic modulus after 14 days

moist curing and possibly with a decrease of the

70/14-day ratio.

(7.7) An increase in K2O was associated with an increase of the dynamic modulus after 14 days

moist curing and after the 8-week drying period

for the Series A concretes. The coefficient was of doubtful significance for the Series 0 concretes.

(7.8) An increase in MgO is probably associated

with an increase in dynamic modulus after 4 and

8 weeks of drying.

(7.9) An increase of air-permeability fineness was associated with a decrease of dynamic modulus after 4 and 8 weeks of drying and after the 4

weeks resoaking for the Series 0 concretes and

probably for the Series A concretes.

(7.10) An increase of the loss on ignition of the

cements was associated with an increase of the

dynamic modulus after the 8-week drying period,

and with a decrease in the ratios of dynamic modulus at all conditions.

(7.11) The use of trace elements having coef./

s.d. ratios greater than 1.0 as independent variables, together with other commonly determined

independent variables in equations, generally re- sulted in a significant reduction of variance when

124
the concrete was moist. After 4 or 8 weeks drying

in laboratory air there was no evidence that the

trace elements had a significant effect. With a few

exceptions, the coefficients of the trace elements were of doubtful significance.

(8) The use of the major oxides instead of the

major compounds, but with other commonly determined independent variables and trace ele- ments, generally resulted in equations with about

the same estimated standard deviation.

(9) Equations calculated for concretes made of the NAE cements resulted in coefficients, coef./

s.d. ratios, and S.D. values in reasonable accord

with those calculated for the concretes made of the AE + NAE cements.

(10) There was no significant relationship between the dynamic modulus of the concretes at 14 days and the dynamic modulus of 1:2.75

(cement to graded Ottawa sand) mortar prisms

at 7 days.

9. References

[1] Whitehurst, E. A., Evaluation of Concrete Properties

from Sonic Tests, ACI Monograph No. 2, Amer.

Concrete Inst., Detroit, Mich., 1966.

[2] Jones, R., Non-Destructive Testing of Concrete, Cambridge University Press, Cambridge, 1962, Chapter 2.

[3] Powers, T. C, Measuring Young's Modulus of Elasticity by Means of Sonic Vibrations, Proc. Amer.

Soc. for Testing and Materials, Vol. 39, Part II, 1938, pp. 460-467.

[4] Thomson, W. T., Measuring Changes in Physical

Properties of Concrete by the Dynamic Method,

Proc. Amer. Soc. Testing and Materials, Vol. 40, 1940, p. 1113.

[5] Hornibrook, F. B., Application of Sonic Method to Freezing and Thawing of Concrete, ASTM Bulletin, No. 101, Dec. 1929, p. 5.

[6] Report on Cooperative Freezing and Thawing Tests

of Concrete, Highway Research Board Special

Report No. 47, 1959.

[7] Investigation of Durability of Concrete Exposed to Natural Weathering, Report No. 5, Summary of Results 1936-1953, Tech. Memo No. 6-226, U. S. Army Corps of Engineers, Waterways Experiment

Station, Viclcsburg, Mississippi, May 1954.

[8] Evans, D. N., Blaine, R. L., and Worksman, Paul,

Comparison of Chemical Resistance of Supersulfate

and Special Purpose Cements, Proc. of Fourth

International Symposium on the Chemistry of Cement, Washington, 1960, Vol. 2, p. 871, Nat.

Bur. Stand. (U.S.), Monogr. 43, 1125 pages (origi- nally issued Sept. 1962, reprinted Feb. 1964).

[9] Kaplan, M. F., Effects of Incomplete Consolidation on Compressive and Flexural Strength, Ultrasonic Pulse Velocity, and Dynamic Modulus of Elasticity

of Concrete, Journal Amer. Concrete Inst., Mar.

1960, Proceedings, Vol. 56, p. 853.

[10] Long, B. G. and Kurtz, H. J., Effect of Curing Methods

upon the Durability of Concrete as Measured by

Changes in the Dynamic Modulus of Elasticity, Proc. Amer. Soc. for Testing and Materials, Vol. 43, 1943, p. 1051.

[11] Philleo, R. E., Comparison of Results of Three Methods

for Determining Young's Modulus of Elasticity of Concrete, Journal Amer. Concr. Inst., January 1955,

Proceedings, Vol. 51, p. 461.

[12] Vaishnav, R. N., and Kessler, C. E., Correlation of Creep of Concrete with its Dynamic Properties, T. and A.M. Report No. 603, Univ. of Illinois, Urbana, 111., September 1961.

13] Chang, T. S. and Kesler, C. E., Correlation of Sonic

Properties of Concrete with Creep and Relaxation,

Proc. Amer. Soc. Testing and Materials, Vol. 56, 1956, p. 1257.

[14] Kesler, C. E. and Higuchi, Y., Determination of Compressive Strength of Concrete by Using its Sonic

Properties, Proc. Amer. Soc. for Testing and Materials, Vol. 53, 1953, p. 1044.

[15] Standard Method of Test for Fundamental Transverse

Longitudinal and Torsional Frequencies of Concrete

Specimens, ASTM Designation C215-60, 1968 Book

of ASTM Standards, Part 10, Amer. Soc. for Testing

and Materials, Philadelphia, 1968, p. 155.

[16] Interrelations Between Cement and Concrete Properties, Part 1 —Section 1, Materials and techniques,

Blaine, R. L., Arni, H. T., and Foster, B. E.; Section

2, Water requirements of portland cements, Blaine, R. L., Arni, H. T., and Clevenger, R. A.; Section 3, Occurrence of minor and trace elements in portland

cements, Blaine, R. L., Bean, Leonard, and Hubbard, Elizabeth K.; Nat. Bur. Stand. (U.S.), Bldg.

Sci. Ser. 2, 40 pages (Aug. 1965).

[17] Interrelations Between Cement and Concrete Properties, Part 2—Section 4, Variables associated with

expansion in the potential sulfate expansion test, Blaine, R. L., Arni, H. T., and Evans, D. N.;

Section 5, Heat of hydration of portland cements,

Blaine, R. L., and Arni, H. T.; Section 6, Variables

associated with small autoclave expansion values of portland cements, Blaine, R. L., and Arni, H. T., Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 5, 46 pages

(July 1966).

[18] Interrelations Between Cement and Concrete Properties, Part 3—Section 7, Compressive strength of mortars, Blaine, R. L., Arni, H. T., and DeFore,

M. R.; Section 8, Compressive strength of steamcured Portland cement mortars, Blaine, R. L., Arni, H. T., and DeFore, M. R.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 8, 101 pages (Apr. 1968).

[19] Interrelations Between Cement and Concrete Properties, Part 4—Section 9, Shrinkage of hardened

portland cement pastes, Blaine, R. L., Arni, H. T., and Evans, D. N.; Section 10, Shrinkage and ex- pansion of concretes, Blaine, R. L., and Arni, H. T.; Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 15, 78 pages (Mar. 1969).

125
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4. TITLE AND SUBTITLE

Interrelations between Cement and Concrete Properties, Part 5>

Freezing- and -Thawing Durability, Saturation, Water Loss and

Absorption, Dynamic Modulus

5. Publication Date November 1971

6. Performing Organization Code

7. AUTHOR(S) , . ^ „ rr, ^ . R. L. Blaine and H. T. Ami 8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

1 1» Contract/Grant No.

12* Spon s onn ^ Or^ 3S\ izslZ ion snci Add rc s

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16. ABSTRACT (A 200-word or less fact ual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The concretes described in earlier parts of this series were subjected to laboratory

freezing and thawing tests, and measurements were made of the weight loss, dynamic

modulus, durability factor, and number of cycles required to reach hO percent reduction in dynamic modulus. Companion specimens were subjected to drying and subsequent

soaking in the laboratory and to dynamic modulus tests at variou.s ages and moisture

conditions. The effect on these properties of a large number of variables connected

with chemical and physical properties of the cements and with properties of the con- cretes was studied by raultivariable regression techniques. Air content of the con- cretes and degree of saturation generally had the greatest effect on the measurements.

In general, minor constituents and trace elements did not show significant relationships with the measured properties, but there was evidence that some of the variables,

such as alkali content, water cement ratio, slump, and possibly setting time might

have influenced durability through an effect on the air-void system. Specimens stored

in the fog room after the freezing- and-thawing tests generally regained most or all of

their original dynamic modulus. There were significant differences between cements

with respect to regain of dynamic modulus (autogenous healing), with the non-airentrained cements gaining more than the air-entraining cements, on the average.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Absorption; autogenous healing; durability factor; dynamic modulus of elasticity;

saturation coefficient.

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