1
National Bureau ^^t^^s^A ^ Library, M. Bldg |TS1Z9 : , >

SEP 2 0 1955 Tf^^^S^

BUILDING SCIENCE SERIES £m

Reference book not to be

taken from the library.

Interrelations

between

Cement & Concrete

Properties

PARTI

/ W \ U.S. DEPARTMENT OF COMMERCE

% j National Bureau of Standards
Announcing The —Building Science Series

The "Building Science Series" disseminates technical information developed at the

Bureau on buUding materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural

and environmental functions and the durability and safety characteristics of building

elements and systems.

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

Structure Reports (1938-59), are directed toward the manufacturing, design, and construction segments of the building industry, standards organizations, officials responsible

for building codes, and scientists and engineers concerned with the properties of building

materials.

The material for this series originates principally in the Building Research Division

of the NBS Institute for Applied Technology. Published or in preparation are:

* BSS-1. Building Research at the National Bureau of Standards. (In preparation.)

* BSS-2. Interrelations Between Cement and Concrete Properties, Part I. (This

publication.)

* BSS-3. Doors as Barriers to Fire and Smoke. (In preparation.)

[See mailing list announcement on last page.]
UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

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

Interrelations Between Cement and

Concrete Properties, Part 1

Materials, Techniques, Water, Requirements and Trace Elements

R. L. Blaine, H. T. Arni, B. E. Foster, et al.

Building Research Division

Institute of Applied Technology

Building Science Series 2

Issued August 20, 1965

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 - Price 35 cents
RELATED PUBLICATIONS

NBS Monograph 28—Causes of Variation in Chemical Analyses

and Physical Tests of Portland Cement—25 cents*

NBS Monograph 43—Chemistry of Cement

Proceedings of the Fourth International Symposium—Washington

1960. Presented in two volimies. Volume I—$6.50. Volume

II—$6.25. The two volumes at $12.75 a set.* (Originally

issued September 1962, and reprinted Feburary (1964).

*Order publications from Superintendent of Documents, Government Printing

Office, Wasiiington, D.C., 20402. (For foreign mailing, add one-fourth of the price of the publication.) n

Library of Congress Catalog Card Number : 64-60095
Foreword

In studies at the National Bureau of Standards on the interrelations between cement and concrete iDroperties, many different tests were made on a

large number of portland cements. Because of the large quantity of data

obtained and the variety of tests performed, the results of these studies are being

published as a series of related sections each dealing with different aspects of

the properties and analyses.

This publication presents the first three sections which deal primarily

with the materials, general test methods and statistical analyses employed

throughout the series. Reference will be made to this first section in subsequent

parts of the series. Included in this first part are a section on water requirements of neat pastes, mortars and concrete and a section on the occurrence of

minor and trace elements in portland cements. Other parts will include

studies of sulfate expansion, heat of hydration, autoclave expansion, compressive

strength after normal and steam curing, shrinkage, absorption, freeze-thaw

durability, as well as the effect of outdoor exposure on concrete specimens.

A. V. AsTiN, Director.

in
Contents

Page Foreword m

Section 1. Materials and techniques

R. L. Blaine, H. T. Ami, and B. E. Foster 1

Section 2. Water requirements of portland cement

R. L. Blaine, H. T. Arni, and R. A. Clevenger 13

Section 3. Occurrence of minor and trace elements in portland cement

R. L. Blaine, Leonard Bean, and Elizabeth K. Hubbard 33

IV
Section 1. Materials and Tecliniques

R. L. Blaine, H. T. Arni, and B. E. Foster

The studies of the interrelations between cement and concrete properties are presented

in a series of related articles. This first section presents the type classification of the cements and the areas from which they were procured togetlier with the tests performed on

the cements and concretes. Also presented are the methods employed in the statistical treatment of the data and a discussion of the significance of the various statistical tech- niques employed in the following sections dealing with specific aspects of the interrelations between cement and concrete properties.

Contents

Page

1. Introduction 1 2. Cements and concretes 2

3. Nomenclature . 3

4. Statistical treatment of the data 4

4.1. Preliminary exploratory techniques 5

4.2. Fitting of regression equations 6

4.3. Further exploratory techniques 8

5. Limitations on interpretation of statistical studies.- 9

6. Summary and conclusions 11

7. References 11

1. Introduction

The study of the interrelations between cement

and concrete properties on which this and succeeding sections are based was started in 1953. The

purposes for which it was undertaken were : ( 1

) To

review the properties of cements then being manufactured ; (2) to study further the extent to which

specification tests could predict the properties at

later ages of the cements and concretes; and (3) to

discover, if possible, better criteria for such predictions. In order to achieve these ends, 199 portland

cements of the various specification types were

procured from different manufacturers and areas of the United States including a few from other

countries.

This first section presents information on the

sources and types of cements, and a general description of test procedures used in the study.

Also presented are the statistical methods employed in analyzing the data and a discussion of

the various techniques used. The material in this

section will be referred to in the following sections

of this series of papers.

This project produced a collection of data so vast (data on the field specimens are still being

acquired) that no adequate analysis was feasible

until a modern high-speed digital computer be- came available. The study has certain characteristics common to many others of a similar nature

over the country. Some of the data reflect the imposed restraints of manufacturing to specifications, which often severely limits the range of the

variables that are studied. Also, many of the variables are more or less correlated in the values that

are available, and this further complicates the

problem of interpretation.

It is probably true that, per unit of data, such

accumulated records have a low efficiency in yielding information in comparison with carefully

planned experiments. In the cement and concrete

field, however, synthetic cements formulated to certain compositions, although useful and important in studying the underlying reactions involved

in cement manufacture and use, do not really

reflect in performance the "commercial" product,

and there is at present no alternative to using the

records of actual cements in an endeavor to relate

performance to various physical and _ chemical

tests. The present study is an exploration which

aims to put on record a large array of combinations

of variables that were tried as predictors of per- fprmance, and it is hoped that some of the indications arising from this work will point the way to some avenues of fruitful research for other

investigations.

A number of statistical devices, of varying degrees of power and sophistication, have been used

to determine what factors may be associated with

properties of the cements and concretes, and to what extent. The most refined tool, used in all cases, was the fitting of multivariable regression

equations to the data, with various simpler techques being used previously to determine what variables out of the many available might be tried in

the fitted equations. The various techniques will
be explained in more detail in this section in order

to give the nonstatistically trained reader an

understanding of what was done and of the significance of the I'esults. In the Fourth International Symposium on the

Chemistry of Cement held in Washington, D.C.,

in 1960.^ [1] a number of articles were presented

stressing the importance of certain minor and trace elements in their effect on the properties of portland cements. There have also been other reports on the effects of these elements [2, 3, 4]. Con2. Cements

The cements used in this investigation were, for

the most part, portions of samples submitted in

1953 and 1954 for test for compliance with Federal

specifications. However, some of the cements of

different types were donated by the manufacturers

and some were purchased from dealers. The number of cements from different areas is listed in

table 1-1. The cements were classified principally on the

basis of their chemical composition. Tlie number

of cements in each of the type classifications is presented in table 1-2. Each of the cements was thoroughly mixed in a blender when available or by rolling on a suitable

sheet of plastic. The cements were stored in sealed

metal containers until tested. In addition to the usual specification acceptance

tests, other test were made, which included spectrochemical determination of minor and trace ele- ments, mortar strength tests at ages up to 10 years, modulus of rupture and dynamic modulus of elasticity for mortar specimens, potential sulfate ex- pansion, shrinkage of neat cement bars, and time

of breaking in a ring shrinkage test described in

future sections.

Table 1-1. The number of cements from each of the various areas indicated

No. of cements Location

33 Eastern Pa., Md. New Yorlf, Maine.

Ohio, Western Pa., W. Va., Mich.

111. Ind., Ky., Wis., Ala., Tenn.

Va., Ga., Fla., La., S. Car., Miss. Iowa, Eastern Mo., Miim., S.D., Kans. Western Mo., Neb., Okla., Ark., Tex.

Colo., Ariz., Mont., Utah, Idaho Northern Calif. Southern Calif. Wash., Ore. other than USA

1818

24

13

19

15 _ 1112

1217

7

Chemical analyses of these cements were made

at either the Seattle or the Washington laboratories of the National Bureau of Standards by the

optional methods outlined in Federal Specifications SS-C-158C [6], except that the sulfur-trioxide determinations were made by the gravimetric method, sodium and potassium oxides were

1 Figures in brackets Indicate the literature references at the end of this section, p. 11.

sequently, part of the work of this study has been

devoted to a search for significant relationships

between the amounts of these elements and the

various properties.

In view of the number of properties and tests involved, it has appeared desirable to divide the

subject matter into sections, each concerning a different subject. A series of sections will therefore

be presented dealing with different properties, such

as water requirements, minor constitutents, potential sulfate expansion, shrinkage, heat of hydration, strength, freeze-thaw durability, etc. and Concretes

Table 1-2. The number of cements of each of the type classifications

Type cement Number of cements

I __. 82 lA 8 II *68 IIA *3

III... ***20 IIIA 3 IV _._ 3 V 12

*16 of these were classified as type I In 1953-54 at the time of procurement.

**1 of these was classified as type lA at the time of procurement. ***Some of these cements would also meet the present requirements for moderate sulfate resisting high early strength cements [5].

determined by the standard Federal and ASTM

flame-photometric methods [6, 7], and strontium

oxide was determined by means of the flame photometer as described by Diamond [8]. Other

chemical elements present in minor quantities were

determined by a semiquantitative spectrochemical

method which wilFbe more fully described in a subsequent section.

The quantities of water used for normal consistency of neat cement pastes and those necessary

to produce a 1 : 2.75 cement to graded OttaAva

sand mortar and 1 : 4 standard Ottawa sand mortar of standard consistency were determined by

procedures outlined in Federal Test Method Standards SS-C-158c [6] and the corresponding

ASTM methods of test for Hydraulic Cement Mortars [9, 10, 11], in effect at that time. The toler- ances on the flow values were chosen less than

those permitted by the specifications in that the

amount of water required for a flow of 90 ±5 was

used for the 1 : 4 mortars and an amount of water

required for a flow of 110 ±5 was used for the

1 : 2.75 mortars. Three batches of 1 : 2.75 cement

to graded Ottawa sand mortar were made of each

of the cements in order to obtain the necessary

number of test specimens. Percentage flow values were obtained on each batch and the average of

these flow values reported. The values reported

for water used for the 1 : 4 cement to 20-30 Ottawa

sand mortar as well as those for the normal consistency of the neat cements were generally the

results obtained in single determinations for the

respective properties of each cement. Although

most of these tests were made in the Washington

2
Laboratory, some were made at the branch laboratories at Allentown, Pa., Denver, Colo., San Francisco, Calif., and Seattle, Wash. Kegularly con- ducted inter-laboratory tests on another series of

cements as well as calibrations of equipment and

techniques were employed to minimize as much

as possible laboratory and operator differences.

More detailed descriptions of the test metht ds

will be presented when necessary in following sec- tions dealing with specific properties.

Two series of concretes were made from these

cements in the Washington laboratory. One series was made with a constant water-cemeut ratio of

0.635. Preliminary tests had indicated that this

would give a concrete having approximately a 5-in. slump. A second series was made in which, if necessary, only the water was varied to obtain concretes of 5 ± 1-in. slump. In both series the ratio of

cement to aggregate was held constant, and the

ratio of fine to coarse aggregate was held at 1 : 1 by

absolute volume throughout. The concretes pre- pared were of a mix design which, in preliminary

tests with a particular cement, had produced concrete with a 51/2-bags-per-cubic-yard cement factor

and 0.Y5 percent air content. A high quality rounded quartzite coarse aggregate (White Marsh) and a sand from the same

source were used for making the concretes. The

aggregates were dried, separated to the various

sizes and recombined when batched. The fineness

modulus of the sand was 2.82. The gradation of

the sand used in the concretes is presented in table

1-3.The fineness modulus was 6.82 for the coarse aggregates, and 4.82 for the combined aggregates.

The gradation of the coarse aggregate is given in

table 1-4. Table 1-3. Sand gradation used in concretes

Sieve-size Percentage

#4-#8 18

1720

25

146

#8-#16 _ _ _ #16-#30 - #30-#50

#50-#100 - pass #100

Table 1—4. Gradation of coarse aggregate used in concretes

Sieve-size Percentage

?4-l in 1035

27

28

M-?4 inin..

.

. U-H in

The sand and gravel were soaked overnight before preparation of the concrete. The concrete was prepared in a tilting drum

mixer with a rated capacity of 1 ft The soaked

sand and gravel and the water were mixed P^

min. The cement was then added and mixing

continued for 2 min. The mixer was stopped for

3 min, after which the concrete was remixed for one additional minute. Each batch of concrete was prepared in a clean, moistened mixer. Previ- ous tests had indicated that approximately 3.2 lb of cement-sand-water mortar was retained by the

mixer when emptied. Properly proportioned

amounts of these materials were added to each

basic mix to provide for buttering the mixer so that each batch of concrete delivered contained

18.80 lb cement, 56.95 lb sand (saturated surface

dry basis), 57.00 pounds coarse aggregate (saturated surface diy basis) and 11.95 lb of water for

the constant water cement ratio concrete, or a proportionate quantity of water in the constant slump

concretes. After mixing, the batch was discharged

into a tared pan, weighed, and adjusted to the

correct delivered weight by adding mortar scraped

from the mixer or subtracting mortar from the

pan. The batch was then remixed with a shovel.

The slump and weight per cubic foot were determined for each batch of concrete in accordance

with ASTM Designations C 143-52 [12] and

C 138-44 [13].

The desired nominal slump of the concrete mixes was 5±1 in. If the first batch of concrete prepared with the constant water-cement ratio was

outside or close to the limits of this tolerance, the

amount of water for the second batch was adjusted

to obtain a concrete with the desired slump.

Otherwise, the same amount of water was used

for both batches.

From the mix px-oportions, weight per cubic

foot, known specific gravities of aggregates and

water, and assumed specific gravity of 3.15 for all cements, the air contents and actual cement factors

of the batches were calculated in accordance with

the requirements of ASTM Designation C 138^4

[13].

Shrinkage, expansion, absorption, dynamic

modulus of elasticity, and freeze-thaw durability

tests were made on the concrete specimens, and

companion specimens were exposed in the field. Length change, weight, and dynamic modulus

measurements have been made on the latter at periodic intervals. The test methods will be described in the following sections dealing with these

properties.

3. Nomenclature

The nomenclature customary in cement technology, viz, C3A, C3S, CgS, and C4AF, is used in

this and the following sections in this series to refer to the potential compound compositions of

the cements calculated by standard procedures

presented in Federal and ASTM specifications for

Portland cements [ 14, 15] . The letters C, A, F, and

S will be used in referring to CaO, AI2O3, FesO.s,

and SiOs, respectively. The A/F and S/(A+F)

ratios were calculated from the percentages of the

oxides AI2O3, FeaOs, and Si02. In the C/S ratio,

the CaO was corrected for the amount of CaO com-
bined with the SO3. In the Lea-Parker ratio

[16] the CaO corrected for the amount combined

with the SO3 was divided by the sum of 2.8 SiOa +

1.18 AI2O3 + O.65 FeaOs. However, no corrections were made for the free-lime content of the cements. The following abbreviations and subscripts as defined below will be used in this and other sec- tions of this series of articles. Wi= The amount of water used for normal consistency of the neat cement paste expressed in per- centage by weight of the dry cement.

W'2=The amount of water used for standard

consistency of the 1 : 2.75 cement to graded Ottawa

sand mortars expressed in percentage by weight

of the dry cement.

W3 = The amount of water used for standard

consistency of the 1 : 4 cement to 20-30 Ottawa

sand mortars expressed in percentage by weight

of the dry cement.

A3 =The air content of the 1 : 4 cement to 20-30

Ottawa sand mortars of standard consistency ex- pressed in percentage by volume of the mortar.

84= The slump in inches of concretes made with

a water-cement ratio of 0.636. (The standard 12-

in. slump cone was used.)

A4=Th6 air content of concretes made with a water-cement ratio of 0.635 expressed as a percentage by volume of the freshly made concrete. W5 = The water-cement ratio (W/C) used for

concretes having a 5 d=l-in. slump. The ratio of

water to cement was calculated on a weight basis. A5 = The air content of the concretes having a slump of 5 ±1 in. expressed as a percentage by

volume of the freshly made concrete. APF= Fineness in sq cm per gram as determined by the air-permeability method.

Wagn= Fineness in sq cm per gram as determined by the Wagner turbidimeter method.

Loss = Loss on ignition as determined by standard ASTM and Federal Specifications for portland cement [6, 7].

Insol= Insoluble residue as determined by

standard ASTM and Federal Specifications for

4. Statistical Tre;

The data obtained were treated statistically

using a digital computer in order to fuid and

evaluate significant relationships between certain

properties or the dependent variables and various

independent variables, which included chemical

composition, minor constituents and trace elements

and the interrelation between the properties of the

cements and concretes. This section describes the statistical techniques

which will be used in subsequent sections to ex- plore the relationships in tlie data. The aim has

been to explain the procedures used in sufficient detail to serve as an aid in understanding what

was done without reproducing in detail material

" References to tables and figures in this section refer to tables and figures in section 2 which follows this section.

Portland cements [6, 7].

Alk = Total alkali (expressed in terms of %

Na20) = % Na20 + 0.658% K^O. (Na^O refers

only^ to the sodium oxide and does not include

the potassium oxide.)

Normal consistency = Term used only for the

neat pastes and is defined in ASTM and Federal

cement specifications [6, 9].

Standard consistency = Term used to describe

the 1 : 4 and 1 : 2.75 cement-sand-mortars having

flow values on the standard 10-in. flow table as required by ASTM [10, 11], and Federal Specifications [6], for these mortars for the air entrainment and strength tests, respectively. (As pre- viously indicated the tolerances of the flow values were chosen less than those specified for standard

consistency.)

NAE= Non-air-entraining cements. AE=Air-entraining cements. AE -I- NAE=Air-entraining plus non-air-entraining cements. Other symbols for the various dependent variables will be described in the sections where they

are used.

In addition, the following statistical terms will

be used throughout this Monograph. They will be

described more completely in the following section.

S.D. = Standard deviation calculated from the

residuals of a fitted equation, or the standard deviation about the average.

s.d. = Estimated standard deviation of the coeffi- cient of an individual independent variable when

used in a fitted equation.

Coef./s.d. or Coefficient/s.d. = Ratio of the esti- mated coefficient (of an independent variable used

in an equation) to its estimated standard deviation.

"F" = Fisher's ratio of variance estimates. Critical "F" values were obtained from tables pre- sented in most textbooks on statistics. See ref. [18] pp. 6-14 to 6-16.

"?^" = Student's "t". Critical values were obtained from tables presented in most textbooks on

statistics. See ref. [18] , pp. 3-23 to 3-26.

nent of the Data^

which is presented better in standard statistical

texts. The reader who is uninterested in these

procedures or familiar Avith statistical techniques

can, it is hoped, skip the section and still derive an understanding of the relationships which were

discussed.

The principal objective of the study of these

data was to seek significant relationships between

certain dependent variables, such as strengths of

mortars and concretes, water requirements, resist- ance to freezing and thawing damage, etc., and

one or more of a large number of independent

variables. The indej^endent variables included

such properties as chemical composition, amount

of air in mortars and concretes, etc. A second objective consisted of studies of the

relationship of the usual laboratory tests, which

4
are normally of short duration, to the long-term

behavior of cement mortars and concretes. The main technique used to attain the above

objectives was the calculation by least squares

methods of the coefficients of regression equations

using the dependent variables with one or more

independent variables. Standard deviations for

the individual coefficients and for the fit of the

individual values to the equation as a whole were

obtained with each equation, and were used to evaluate the significance of the individual coeffi- cients and of the equation.

The development of multi-variable regression

equations is to some extent a trial and error process. The evaluator of the data must decide before

fitting an equation, first, what the form of the

equation shall be (first, second, or higher degree,

exponential, etc.), and second, how many and what:

properties shall be used as independent variables.

The initial choice is guided by judgment based on

experience with, ana knowledge of, the materials

and properties involved. In this study various

preliminary statistical tests were used as aids in

deciding what variables and relationships it might

be advantageous to try, especially in exploring

relationships and variables which had not been

adequately investigated previously. Then, after

fitting the equation or equations, statistical techniques were used to determine which equations

had resulted in meaningful descriptions of rela- tionships, how^ meaningful, and whether one equation was superior to another in this respect.

In view of the above points, this discussion is divided into three main headings under which the

statistical techniques used are described: (1) Preliminary Exploratory Techniques—used in the

search for likely relationships and variables, (2)

Estimation of Coefficients of Regression Equations—the essential part of the study, which in- cludes both the actual calculation of the estimated

coefficients of the equations by least squares

methods and the determination of the significance

of those coefficients and equations, and (3) Further

Exploratory Techniques—used in a search for

further independent variables which it might be

advantageous to use to improve the significance of an already determined relationship.

4.1. Preliminary Exploratory Techniques

_ The frequency distributions of the values of the

different independent variables were determined.

The frequency distributions are given in tables

I (see for example tables 2-1 and 2-2 in the second

section of this publication) showing the total number of values included between the limits of vari- ous ranges of the values of that variable. Most

i of these distributions conformed to the normal dis- tribution rather closely. The frequency distribution, grand average, and standard deviation of

each of the dependent variables was also determined. The average and standard deviation are

helpful in determining the significance of an equation fitted later on.

748-580 O - 65 - 2

Using the computer, a large number of plots were made of dependent variables versus each of

a series of independent variables and in some cases against different functions of the independent

variables, such as the square, square root, logarithm, or their reciprocals. In these plots, instead

of plotting all points, the values of the two variables were arranged in descending order of the

dependent variable, divided into 12 equal groups,

and the average of each group calculated. (If the

total number was not an integral multiple of 12,

the remainder was added to the sixth group.)

The 12 pairs of averages were then plotted.

Examples of two individual plots as obtained

are presented in figures 2-1 and 2-2. In figures

2-3 and 2-4 the trends of a large number of such

plots are sketched in row (2). These sketches

show the apparent trend and shape of the rela- tionship. In row (3) of figures 2-3 and 2-4, the

apparent relationship is further indicated by symbols wdiich are explained in the figure. The numbers and ratios in rows (1) and (4) of figures 2-3

and 2-4 relate to two methods, described below,

which were used to evaluate the significance of

relationships shown by the plots.

The graphs were divided into four quadrants

by a horizontal and a vertical line so that there

Avere equal numbers of points above and below

the horizontal line and to the right and left of

the vertical line (figs. 2-1 and 2-2). The ratio

of the sum of the number of points in one pair

of diametrically opposite quadrants to the sum of

the number in the opposite pair of quadrants was

then determined. (The ratio is always given with

the larger number in the numerator.) See figures

2-1 and 2-2 and the rows marked (1) in figures

2-3 and 2-A. A ratio of 6/6 indicates that the 12

points are evenly scattered around the quadrants

and there is little if any relationship between the

two variables. On the other hand, a ratio of 12/0

indicates that all the points are concentrated in one pair of opposite quadrants, and there is probably a good relationship.

A ratio of odd numbers occurred when the two

middle points had the same ordinate or abscissa,

and one of the median lines had to be drawn

through them instead of between them.

The quadrant ratio criterion mentioned above

is a good technique for a rough preliminary examination of plotted points, but is rather insensitive, so far as detection of actual significance is con- cerned when only 12 points are plotted. In order

to obtain a more sensitive criterion, the quadrant

sum method proposed by Olmstead and Tukey

[17] was used.

The quadrant sum method is applied to the same

plots of points divided into quadrants as was used

for the quadrant ratio criterion (figs. 2-1 and

2-2) . The technique is as follows : The quadrants

are designated + , — , + , —, starting in the upper

right-hand quadrant and going clockwise in the

conventional manner. Then, starting at the righthand side of the diagram, points are counted, pro5
ceeding to the left, until the next point to be

counted is on the opposite side of the horizontal

line from the one on which the counting* started. The number of points counted is then recorded

with the sign of the quadrant in which counting

started. For example, in figure 2-1, the point

farthest to the right is in the lower right quadrant

and is followed by three more below the horizontal

line. The fifth point from the right is the single one in the upper right quadrant. The first number recorded is thus —4. This process is re- peated starting from the bottom of the diagram

and counting up until the first point is found on

the opposite side of the vertical line. (In fig. 2-1

again, the first four points from the bottom are

all in the lower right quadrant and the fifth is in

the lower left, resulting in another count of —4.)

Tlie process is repeated starting at the left and

counting to the right, and starting at the top and

counting down. The algebraic sum of the four

numbers thus obtained is the quadrant sum. In

figure 2-1, the sum is (-4) + (-4) + (-3)

+ (-2) = -13.

A quadrant sum with an absolute value of 11 or greater has a probability of occurrence of 5 percent in a random distribution of points, and

is taken as evidence (at the 95% confidence level)

that a random distribution does not exist, and that

there is a significant relationship between the two

variables. In figures 2-3 and 2-4 quadrant sums

for the plots are given in the row marked (4)

.

Apparent linearity or curvature of the plots is also indicated by the sketches in figures 2-3 and

2-4. This information was used to indicate possible functions of the independent variable which

might be tried in the relationship.

4.2. Fitting of Regression Equations

There are a number of standard procedures for

fitting equations by the method of least squares. These procedures will not be gone into here. The

interested reader may refer to references [18] and

[19] or any standard text on least squares or curve

fitting.

The equations were developed in this study by means of a digital computer program, which permitted the fitting of up to 13 independent variables in one equation, without which the amount

of labor involved would have been prohibitive.

The output from the computer for a given equation consisted of the estimated coefficients for all independent variables (including a constant term)

,

and estimated standard deviations for these coefficients and for the fit of the individual values

to the equation as a whole.^ Also included were

a list of all the deviations of the observed values

from the fitted equation; an value,^ which

indicated the significance of the fitted equation;

^ Coefficients, standard deviations, etc., calculated from data

are, in theory, estimates of a true but unknown population pa- rameter. They should be so understood throughout, although the

adjective "estimated" is sometimes omitted.

4 The ''F" value is the ratio of the reduction In variance due to the fitted constants to the variance obtained from the residuals

after fitting the constants. See ref. [18], pp. 6-14 to 6-16.

and a list of the estimated standard deviations of

all of the calculated values.

The equations are presented by giving the esti- mated coefficients and standard deviations in tables, such as tables 2-3, 2-6, 2-10, 2-14, 2-15, 2-19,

and 2-20. For example, (1) in the first line in

table 2-3 expresses the relationship of the per- centage of water used for normal consistency of

neat portland cement pastes (Wi) to four independent variables, viz, air permeability fineness

( APF) , AloOs, CaO, and SO3. Equation 2 in the same table was fitted using the same data as in eq

(1) but with five more independent variables in- cluded, viz, total alkali, copper, phosphorus, zir- conium, and strontium oxide. These equations

could be written as follows:

Wi=4.58-1-0.00139 APF+0.233 AI2O3+O.I96

CaO-f 0.824 SO3

and

Wi=2.07-^0.00144 APF-^0.307 AI2O3-I-O.23O

GaO+0.776 SO3+O.546 Alk-33.8 Cu

-2.58 P-f 6.62 Zr-1.54 SrO.

Beneath each coefficient in the table is given the

estimated standard deviation (s.d.) of that coeffi- cient as calculated from the data. These standard

deviations are estimates of the error of the coeffi- cients. For the number of values involved in most

of the equations in this study an approximate 95

percent confidence interval for a coefficient may be

obtained by multiplying its standard deviation by

tw^o. Thus, if the coefficient is greater in absolute

value than twice its standard deviation, one may

make the assumption that there is a 95 percent

probability that that coefficient differs from zero, and therefore, that the independent variable asso- ciated with that coefficient has a significant effect on the dependent variable in the equation. Note

that all the coefficients in eqs (1) and (2) except

the two constant terms and alkali and SrO in eq

(2) meet this criterion of significance.

Since the work of this study was largely exploratory in nature, a variable was generally eliminated from consideration in subsequent equations

only if its coefficient in a given equation failed to equal or exceed one times the standard deviation

of that coefficient, although this indicates only

about a 70 percent confidence in the estimate of the

coefficient. One of tlie reasons for doing this was

that addition of other variables to an equation, or other changes, usually changed the ratio of coefficient to standard deviation for variables which

were included in both the equations. For example,

in eq (5), table 2-3, CaO has a coefficient of 0.131

which is less than two times its estimated standard

deviation of 0.079. However, in eq (6) in the same table, where five other independent variables

haA'e been included with the previous four variables, the coefficient for CaO is about the same as two times its s.d.
The last column in the tables of equations gives

the estimated standard deviation of the equation

as a whole under the heading S.D. As mentioned

previously, in all the papers of this series the con- vention is followed of using s.d. to designate

standard deviation of an individual coefficient and

S.D. for standard deviation of a fitted equation or

of the values of a single variable. The S.D.'s for

values of the dependent variables are given in notes at the bottom of the tables of equations. The

latter were calculated, by the standard formula,

using the sum of squares of the deviations of all the values of the variable from the grand average.

The S.D. for a fitted equation was obtained, in an

analogous manner, from the sum of squares of the

deviations of the observed values from the corre- sponding values calculated using the fitted equation. In table 2-3, S.D. for eq (1) is 1.149 compared to an S.D. of 1.494 for the 180 values of water

for normal consistency. This is a highly signifi- cant reduction in standard deviation gained by

fitting an equation with four independent variables. In eq (2) a further reduction to 1.045 has

been achieved by fitting five more coefficients. This

is also a highly significant reduction.

In cases where an equation is fitted with one set of variables, and a further reduction of the esti- mated standard deviation is obtained by fitting one or more additional variables with the same

original set, it is possible to assess the significance

of the reduction statistically. This was done for

all such pairs of equations given in tables 2-3, 2-6,

2-10, 2-15, and 2-20, and the results are presented

in table 2-22. The "F'' ratio ^ given in column 3

of table 2-22 must exceed the Critical ratio

in the last column for the reduction to be signifi- cant at the 95 percent level and the critical ratio in the next to the last column to be significant

: at the 99 percent level.

i Another technique that was used to check on

\ the reliability of a fitted equation was to develop

I two more equations with the same dependent and

1 independent variables, but using in the first one

I only the odd numbered values from the array used

I in calculating the coefficients for the original equaI tion and the even numbered values in the second

one. This is illustrated by eq (2) in table 2-3,

I calculated from values from 180 cements, and eqs (2A) and (2B) each calculated from 90, or half

j the original set. These equations were compared

I and if the coefficients of the "odds" and "evens"

are in close agreement, the confidence which can

; be placed on the relationship is enhanced. There

I were a number of cases in which an estimated co-

'[ efficient was larger than its s.d. in the complete

J set but smaller in one of the reduced sets, as in the

case of alkali in eqs (2) and (2A), table 2-3.

i[

However, this usually happened only in cases where the coefficient for the complete set was near

j the borderline of significance. It occurred in very

1 '^'^'^is "F" ratio is the ratio of the reduction in variance due to

1 the additional fitted constants to the variance obtained from the

i residuals after fitting all the constants. See ref. [18], pp. 6-14

I to 6—16.

few cases where the original coefficient was more

than two times its s.d. If the equations were not

in agreement studies were made of the individual

values to determine if one or more of the cements was \'ery different in some respect.

In all cases equations were fitted for a dependent

variable and a set of independent variables using

all the cements (AE + NAE), witliout respect to type classification and then a second equation using

only the non-air-entraining cements (NAE),

again without respect to type classification (table

2-3, eqs (1) and (2) for example). Equations were not developed with the AE cements alone

because there were too few of them to give a significant result, and because of this, inclusion or ex- clusion of the AE cements made little difference

in the results in most cases, unless air content was

an important independent variable.

The number of cements represented in the equations varied, as may be seen from the tables, due

to a number of reasons. Three white portland

cements were, because of their very low iron contents, excluded from many of the statistical studies. Also one or more test values were missing

from some of the variables for one reason or another, and when a test value was missing from

one variable in a set being considered, data for

that cement had to be eliminated from all the other

variables being used. Generally in developing any

series of equations, such as all those in table 2-3,

all cements which had missing values in any of the

variables to be used throughout the set were eliminated before fitting any of the equations. Thus

each equation in the set was based on data from

the same list of cements and could be compared

with more confidence to any other in the same set. Minor constitutents were not determined on all of the cements. In cases where these were used

as independent variables, therefore, the elimination of cements with missing values resulted in

equations which were based on 170 to 180 cements

when both air-entraining and non-air-entraining

cements were used, and about 160 to 165 when only

the non-air-entraining cements were used.

There were cases in this investigation in which some of the values for some of the variables appeared far out of line with the other values and

no satisfactory explanation could be determined

other than possible error in testing or in tran- scribing of test values. In this study, cements

which had a value for a variable which differed

from the average by more than four times the

standard deviation of all values of that variable, were generally deleted from consideration if a study of the test results of that cement indicated

nothing else unique with respect to its properties.

For some equations, the apparent contribution

and range of contribution of the independent variables to the dependent variables were computed.

(See table 2-4.) This was done by multiplying

the upper and lower values for each variable

(col. 2) by the coefficient for that variable (col. 4)

to give the calculated contributions in col. 6. The

7
ranges in col. 6 are the differences between the two

values in col. 5. It must be emphasized that these are not exact values, but only indications estimated

from the equations calculated from the data of

this study. For these computations, an equation

including the trace elements and having a low

S.D. value was usually chosen. Different values

may readily be derived from other equations pre- sented in the tables.

4.3. Further Exploratory Techniques

Once an equation was developed with a given

dependent variable and a certain basic set of independent variables and with estimated coefficients significantly larger than their estimated standard

deviations, the question then arose, would this re- lationship be improved by including others of the

large number of available independent variables

in the same relationship. In particular it was

desirable to investigate the effect of the relationships of the minor and trace elements which were

determined in this study but are not usually determined in cement analyses.

One method of exploring the contribution of

these other variables would be the trial and error method of fitting new equations, adding the other

variables singly and in various combinations.

And indeed, the final test of whether a new variable or combination of variables had a significant

effect was to fit it in the equation and observe

whether a significant reduction in S.D. and significant ratios of coefficient to s.d. for the new variable occurred, together with no loss of significance

for the other coefficients in the equation.

The trial and error method is a time-consuming

process, however, and in order to explore the re- maining variables in a search for likely ones to

fit in the equations, two statistical techniques were

used. Botlx of these techniques were based on the

following assumption. If a given independent

variable has no functional relationship to the dependent variable in a given equation, then the

distribution of the values of the independent variable should be random with respect to the distri- bution of the deviations from the fitted equations.

The deviations from an equation are obtained by

subtracting from the observed values of the dependent variable, the calculated values obtained

by substituting in the equation the sets of observed

values of the independent variables corresponding

to each observed value of the dependent variable.

If the equation exactly fitted all the observed values, of course, all the deviations would be zero and the S.D. for the equation would be zero. This

never happens in any practical case, however, and

the deviations that occur are compounded of two

elements, ( 1

) the irreducible random error of the

testing procedure, and (2) the effects, if any, of

other independent variables which were not in- cluded in the equation.

If the distribution of the values of the variable

is random with respect to the deviations, then

there should be no significant difference between

the average of values of the new variable for

cements associated with large positive deviations

and those associated with large negative deviations, for instance. On the other hand, such a

difference should exist if the new variable is in

part responsible for the deviations in the equations.

The first method used for exploring the situations described above employed the standard Student's test for a significant difference between

averages. See ref. [18], pp. 3-23 to 3-26. In this

method the cements which were responsible for

the 20 positive deviations of the greatest magnitude, the 20 with the negative deviations of greatest magnitude, and the 20 with deviations in the

middle of the distribution (closest to zero in most

cases) in a fitted equation were determined. Then

for the values of each other independent variable

to be examined, two comparisons were made as follows : ( 1

) The average of the values for the 20

cements from the large positive deviation group was compared to the average value of the 20 from

the large negative deviation group. Since the

ones with the largest positive deviations are those

which are highest with respect to the corresponding values calculated from the equation, and those

with the greatest negative deviations are those

which are lowest with respect to the calculated

values, this is called in what follows the "highlow comparison." (2) The average of the large

positive and large negative deviation groups to- gether was compared to the average of the 20 from

the middle group. This is called the "middle-ends

comparison." A significant difference in the highlow comparison indicates that the variable under

consideration may be correlated with the deviations from the equation being studied, and it may

be fruitful to include it as an additional independent variable in that operation. A significant

difference in the middle-ends comparison leads one

to suspect the existence of a nonlinear relationship

between the independent variable and the dependent variable in the equation. In many cases, such

as eqs (1) and (2) in table 2-3, the additional

variables to add to the original equation were

selected in this manner. In both comparisons the "F" test for determination of a significant difference between variances

[18] was used to determine whether the variances

of the two groups of values were sufficiently alike

to make the "?'" test valid. The independent variables tested by these techniques included the oxides, some of the chemical ratios, and all determined minor and trace elements which are listed in a following article. The ";5" test for a significant difference between

averages used in the method described above is sensitive to a single unusually large value in one

of the groups compared. Another difficulty, peculiar to this study, was that for many of the minor

constituents or trace elements, there was an appreciable number of zeros in the data. This did not

always mean that the element was nonexistent in

those cases, but it was beneath the lower limit re-
ported. It sometimes happened that in one or more of the groups of 20 the majority of the values were zero. These and other considerations caused

anomalous results in some instances.

For the above reasons another technique was

used which had the advantage of examining all the values of a variable instead of only three

groups of 20 and which was not ati'ected by single

large values. In this method (table 1-5) all the

values of a variable which were not zero were

tallied on a 3 by 3 grid according to whether they

represented a cement with a high, medium, or low

deviation in the given equation " and whether

they were in the high, middle, or low third of the

distribution of values for the variable. In addition the zero values which corresponded to high,

middle, and low deviations were tallied and the row sums for the nonzero values determined. Proportions in each category were also calculated.

This test was dubbed the "tic-tac-toe" test because

of the resemblence of the grid to the old-fashioned

game.

As an aid in assessing the meaning of these

"tic-tac-toe" distributions, a chi-square statistic w^as calculated for each one. One of the uses of

the chi-square test [21] is to measure conformance

of an observed distribution with some expected

distribution.' In our case the assumption is that

the values of the independent variable in question

are randomly distributed with respect to the deviations from the equation and therefore the numbers tallied in the nine cells of the grid should be

approximately equal and the numbers of zeros should be divided in thirds. (The chi-square is calculated only for the distribution of nonzero

values.) Any significant departure from the ex- pected uniform distribution represents evidence

that there is some relationship between the variable

and the deviations and causes an increase in chi- square. Table 1-5 shows a sample printout from the

computer program which was used to calculate

the "tic-tac-toe" distribution, chi-square, high-low

comparison, and middle-ends comparison for any

chosen variable and the deviations from a chosen

equation. (This particular evaluation was for

lota] alkali as an independent variable compared

lo tlie deviations from an equation using 24-hr

shrinkage on drying and was developed for a later

article in this series.) In this example there did

not happen to be any zero values for the independent variable (alkali) and the expected number in each cell of the 3 by 3 array would be

between 17 and 18, one-ninth of the total number

of 158. Note that the number is considerably

higher than expected in three cells along one di- agonal of the array, indicating that high values

of alkali were associated with observed values of

expansion above those calculated from the equation, and low values of alkali were associated with

the large negative deviations. The chi-square of

19.9 is significant at the 95 percent level. The

"^" values for the high-low and middle-ends comparisons, however, did not show any significance

in this case. Evidence of significance from either tlie ";5" test, the "tic-tac-toe" or chi-squai-e tests was used in se- lecting additional independent variables to be

added to already fitted equations. If the additional independent variable did not meet the cri- teria used it was not included in the reported

relationships.

Table 1-5. 24-Hour shrinkage versus total alkali Number of values =158 Number not zero = 168

Deviations

High. /Number

"IProportion. Medium /Number ivi eaium.. . [proportion . _

.

Tnnr /Number.... Low tProportion- Totals

Values of variable

High Medium Low Total Zero

23

0. 4423

12

0. 2308

17

0. 3269

52

13

0. 2407

30

0. 5556

11

0. 2037

54

16

0. 3077

12

0. 2308

24

0. 4615

52

52

0. 3291

540.3418

52

0.3291

168

Chi square = 19.92. Hi-lo comparison ( 19, 19 D . F.) ,

' =0.0135, ratios of variances = 1.090, 0.918. Middle-ends comparison (38,19 D.F.), "<" = —0.272, ratios of variances =

1.892, 0.629.

5. Limitations on Interpretation of Statistical Studies

Some of the problems associated with the statistical analysis of a large amount of data as developed in this program have been dealt with in the

introduction. It was pointed out that these studies were exploratory in nature and that the statistical devices had varying degrees of power and sophistication. In the preceeding subsection the various

statistical techniques used were described and

some of their limitations noted. Further limitations and problems associated with the interpretation of the results are presented in this subsection.

Plotting the dependent variable and various

single independent variables using the averages

0 In this context high, medium, and low refer respectively to the upper, middle, and bottom third when the deviations are ranked in order from greatest positive to greatest negative.

' See ref. [21], pp. 174-179.

of the 12 groups as previously indicated, provided

a simple graphic method of presentation of the

trends involved. The quadrant ratios and quadrant sums were computed in order to further eval- uate these trends and to indicate which variables

should be used in an equation. However, there

were, as will be noted in the following sections,

many discrepancies between the results of these

evaluations and the more sophisticated least squares method used to evaluate the combined ef- fects of a number of variables. For example, in

section 2 on water requirements, eq (2) of table

2-14 and figure 2-2 represent relationships between

the same pair of variables. Figure 2-2, however,

appears to indicate a definite curvature, while

eq (2) is linear, and if plotted on the coordinates

9
of figure 2-2 would not appear to fit the plotted 12

points. This apparent discrepancy is due to several characteristics of the data such as: (1) The

scatter of the individual points, which causes uncertainty in the coefficients of an equation developed for all of them, (2) the method of averaging

used in developing the plots, and (3) the narrow

range of the values of the variables, which results in a small difference in shape between a linear plot

of the variables and, for instance, their squares. A second-degree equation developed with these

two variables did not show increased significance over tlie linear one. Whereas some of these discrepancies may be

caused by factors which will be discussed later in

connection with individual cases, some may be

caused by an independent variable having a pre- dominant effect. In tlie examples presented from

the following sections on water requirements, the

air-entraining characteristic is such a i^roperty

and there were only 14 cements classified as AE.

The effect is shown in frequency distribution values, in the S.D. values as well as in the comparable

equations computed for the AE + NAE and the

NAE cements. Such effects are more pronounced

in the case of some properties tlian in others. It appeared desirable, even tliough equations could

not be computed for the AE cements by themselves, to include them with the computed equations for the NAE cements. In addition, the

equations were also computed for the NAE

cements. In any statistical studies of this nature, the empirical equations are dependent on the adequacy

of sampling of the population, in this case, all Portland cements. In an attempt to obtain a rep- resentative sampling, cements of the different

types and from as large an area as possible were

included. The chemical analyses indicated fairly

normal distributions of most of the oxides determined. As indicated previously in discussing the

effect of air entrainment, a normal distribution

is not always attained with all properties. The

comparisons of the coefficients for the different

independent variables of the "odds" and "evens"

in an array of cements (assuming representative

sampling) afforded a greater confidence in the

equations when the coefficients were in close agree- ment. Conversely, when discrepancies did occur,

as was the case with some variables having coeffi- cients of marginal significance, the need for further stvidies of those variables was indicated.

Some of the anomalies noted may have resulted

from the chance occurrence of two or more ex- treme values of a variable in one of the two groups.

Other anomalies may have resulted from the

method of treatment of the trace elements many

of which had values below the reporting limit

and were listed as having a zero quantity. In some

instances only a few of the cements had reported

values for some of the trace elements.

Certain other difficulties and problems related

to the nature of portland cement are encountered

in the interpretation of equations such as those

derived and presented in the following sections.

Some problems result from the leeway permitted,

for example, in water used for normal consistency

of pastes and mortars and to the large variability

associated with the test methods. The lack of

information of some of the variables also limited

the attainment of better relationships. Still other

problems arise from the interaction or interdependence of some of the nominally independent

variables.

Some of the quantities measured are quantities

which have been closely controlled in the manufacture of the cement, usually because of specification limits or because experience has shown that

they have a large effect on the finished product.

The range of values of such a quantity when used

as one of the variables in an equation may, therefore, be insufficient to show the relationship be- tween tliat variable and some other property of

the cement or concrete used as a dependent variable. If the range of values of an independent

variable is further limited by computing an equation for only one of the five types of cement, for

example, it may be expected that the reliability

of the estimate of the coefficient of a variable

would be less than if a broad range of a cement

property is used in computing the equation.

The nature of the composition of portland ce- ment is such that there may be a relationship be- tween certain so-called independent variables. For

example, the degree of correlation between the

C3S and C2S in a series of portland cements may

be very high. Also, the AI2O3 content and calculated C3A are" related as are other compounds and

oxides. If there are correlations, such as exists

here, between some of the variables in a multivariable relationship, the equations are not necessarily invalidated, but the contribution of individual independent variables to the dependent

variable cannot be considered apart from the contribution of others. Previous studies on pure

compounds and on cements in which attempts have

been made to increase or decrease one variable at a time have fairly well established the roles of the

principal variables. Equations such as those developed in this study may, however, serve a useful

purpose in predicting certain properties or longterm behavior.

The fact that the number of cements involved

in the study was large and that at least semiquantitative values were obtained for the minor constituents permit us to gain some infonnation rela- tive to the relationship of the latter to cement or

concrete properties. More precisely determined

values are needed both for the minor constituents or trace elements and the test results in general.

However, the fact that some of the minor constitu- ents appear to have a significant relationship to properties of interest may indicate that further

studies of the effect of these elements may be desirable and fi'uitful. No information was available on the tempera-
ture of the clinker formation, the amount of liquid

formed, the oxidizing? or reducing conditions of

burning, nor the rate of cooling of the clinker, all of which are recognized as affecting the properties

of Portland cement. In some cases it might have

been possible to obtain lower S.D. values by the

inclusion of some of these variables if knowledge

of them had been available.

Another factor which is probably involved in

the lack of better or more definitive equations is tlie presence of materials otlier than calcium sul- fate in the gypsum used in tlie portland cements. Such materials could affect tlie calculated com- pound composition values in that the chemical

analysis of a cement may differ from that of the

clinker from which it was made.

6. Summary and Conclusions

This first section has presented general information on the cements, concretes, and tests con- ducted as well as the statistical techniques used

throughout and referred to in subsequent sections

dealing Avith specific aspects of the interrelations

between cement and concrete properties.

The 199 Portland cements of the various type

classifications were procured mostly from different areas of the United States with only a few from

overseas and are believed fairly representative of

Portland cements manufactured at the time of

procurement.

The tests made on the cements and concretes have been enumerated and in some instances,

where the tests and test methods were related to various aspects of the study, the methods used

have been described and will be referred to in subsequent sections. Various exploratory techniques

used to determine the variables associated with the

various properties have been described.

Various techniques were employed in determining and assessing the value of independent variables associkted with the different properties. The

greatest importance was given to computed multiple regression equations with means for evaluating the significance of the different variables and

combinations of variables employed.

After developing an equation with a group of

significant independent variables, additional equations using the same variables were computed for

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

When the coefficients for the "odds" and "evens" were in agreement confidence in the relationships was enhanced.

Some of the limitations relative to the statistical interpretations of the results have been presented

and discussed. Examples of the various techniques used have been presented to indicate their

usefulness as well as their limitations.

The techniques described here may be of help

to others faced with the problem of evaluating

large masses of experimental data.

Acknowledgments are made to the heads of

branch laboratories of the National Bureau of

Standards at Allentown, Pa., Denver, Colo., San

Francisco, Calif., and Seattle, Wash., G. Stiller,

O. H. Cox, O. C. Marek, and Frank Winblade,

respectively, as well as their associates and co- workers and to M. R. DeFore, Leonard Bean, and

R. A. Clevenger and associates in the Washington

laboratory for collecting the cements and making

the many tests involved. Acknowledgments are

also made to D. N. Evans for collecting, checking,

and compiling the data. Special acknowledgments

are made to W. J. Youden and J. M. Cameron of

the statistical engineering section and to members

of the computer section for assistance in planning

the investigation and for suggestions and advice

relative to methods of analyzing the data.

7. References

[1] Chemistry of Cement, Proceedings of the Fourth [8] International Symposium, National Bureau of Standards Mono. 43, Vol. 1, 2, Aug. 1962, U.S. Government Printing Office. Washington, D.C. [9]

[2] Proceedings of the Third International Symposium

on the Chemistry of Cement, London 1952, Cement

and Concrete Association, London. [10]

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

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

[4] F. M. Lea and C. H. Desch, The Chemistry of Ce- [11] ment and Concrete, revised edition, Edv^ard Arnold

(Publishers) Ltd., 1956.

[5] Standard Specifications for Portland Cement, [12] ASTM Designation C 150-62.

[6] Federal Specification SS-C-158c Amendment 1 ; Ce- [13] ments, Hydraulic, Methods for Sampling, Inspection and Testing, May 25, 1954.

[7] Standard Methods of Chemical Analysis of Portland [14] Cement, ASTM Designation C 114-53.

J. J. Diamond, Photometric determination of stron- tium in Portland cement, Anal. Chem. 27, 913, June 1955. Standard Method of Test for Normal Consistency

of Hydraulic Cement, ASTM Designation C 187-

55. Tentative Method of Test for Air Content of Hydraulic Cement Mortar, ASTM Designation C

185-53T. Tentative Method of Test for Compressive Strength

of Hydraulic Cement Mortars (using 2 in. cube

specimens) ASTM Designation C 109-54T. Standard Method of Test for Slump of Portland Ce- ment Concrete, ASTM Designation C 143-52. Standard Method of Test for Weight per Cubic Foot, Yield and Air Content (Gravimetric) of Concrete,

ASTM Designation C 138-44. Federal Specification SS-C-192a, Cements, Portland,

July 2, 1956.

11
[15] Standard Specifications for Portland Cement, ASTM [19] R. T. Anderson and T. A. Bancroft, Statistical TheDesignation C 150-53. ory in Research (McGraw Hill Book Co., Inc., [16] Reference 4, page 158. New York, N.Y., 1952)

.

[17] Paul S. Olmstead and John W. Tukey, A corner test [20] W. J. Dixon and F. .J. Massey, Jr., Introduction to for association. Ann. Mat. Statistics 18, 495, Statistical Analysis, 2d Edition (McGraw Hill (1947). Book Co., Inc., New York, N.Y., 1957).

[18] M. G. Natrella, Experimental Statistics, NBS Hand- [21] Sidney Siegel, Noii Parametric Statistics for the hook 91, Aug. 1, 1963, U.S. Dept. of Comm., NBS, Behavioral Sciences (McGraw Hill Book Co., Inc., U.S. Government Printing Office, Washington, D.C. New l^ork, N.Y., 1956).

12
Section 2. Water Requirements of Portland Cement

R. L. Blaine, H. T. Arni, and R. A. Clevenger

The relationship between cement characteristics and the water requirements of neat cement pastes, mortars, and concretes made with 199 portland cements of different types and

from various areas were studied by fitting multivariable regression equations with the aid of a digital computer. The principal variables which appeared to have the greatest effect on

water requirements were as follows: (1) For neat cement pastes of normal consistency

fineness; (2) for the 1:4 and 1:2.75 mortars of standard consistency—the air content, AljOs,

and silica modulus; (3) for concretes—the air content, AI2O3, and Fe203. The use of A/F

ratios or the potential C3A values in place of the AI2O3 values in the computations resulted in concordant equations. Other commonly determined variables as well as a number of the minor constituents and trace elements also appeared to be associated with the water require- ments to a lesser degree.

Contents

1. Introduction 13

2. Portland cements and concretes 14

3. Statistical treatment of data 14

4. Results of tests 14

4.1. Chemical analyses and fineness of portland cements 14

4.2. Water requirements of neat portland cement pastes 14

4.3. Water requirements of 1:2.75 cement to graded Ottawa sand mortars 15

4.4. Water requirements for 1:4 cement to standard Ottawa sand mortars 19

4.5. Concrete made with a constant water-cement ratio 21

4.6. Concrete with a slump of 5±1 inches 24

4.7. Calculations on high- and low-air cements 28

5. Discussion 28

6. Summary and conclusion 31

7. References 32

1. Introduction

It has long been recognized that the water re- quu-ements necessary to produce comparable

consistency, workability or placeabUity for neat

pastes, mortars, or concretes differ to some extent with different cements. Cognizance has been

given to this property in Federal [1] ' and ASTM

specifications [2, 3, 4] by providing that different

amounts of water be used with different cements

for the neat cement pastes of normal consistency

required for time of set and autoclave tests, as well as different amounts of water with different

cements for the mortars of standard consistency

used for the laboratory acceptance tests, for strength and other properties. The use of differ- ent water percentages with different cements in the laboratory acceptance tests has been justified

because of the relationship of those water-cement

ratios to the water requirements of concretes. However, the degree of correlation of water re- quirements of pastes and mortars with that of concrete has often been questioned. Also, differ- ent laboratories have exhibited some difficulties in obtaining satisfactory agreement with respect to the water requirements for the standard test mortars which, in turn, may lead to variations in test

results. Because of such difficulties, proposals

have been made that better interlaboratory correlation of strength test results would be obtained

if a constant water-cement ratio were used in the

' Figures in brackets indicate the literature references at the end of this paper, p. 32.

laboratory acceptance test mortars. For example, the tentative specification, ASTM Designation C109-43T, later withdrawn, required the use

of 53 percent water with all cements in the 1 : 2.75

cement to graded sand mortar. It was reported

[5] that, with air-entraining cements, flows of such

mortars on the standard 10-in. flow table ranged

from 120 to more than 150 percent.^ Other specifications such as those developed and proposed by

Cembureau and RILEM which are used in some

countries also require the use of a mortar with a constant water-cement ratio. Although many articles have been published

relative to water requirements of cements and

concretes, previously unpublished but relevant

information on this subject obtained as a part of

this study of various interrelations between cement

and concrete properties is presented. It seemed

that with the large amount of data available it would be possible to determine some of the factors

which may contribute to such variations. This

section, which is one of a series on the study of interrelations between cement and concrete properties, deals primarily with the subject to water

requirements of different cements in the different test-mortars and concrete. However, the influ- ence of air contents of the different mixtures wiU

also be considered.

2 A pertinent discussion relative to this article was presented by

Abrams [7]

.

748-580 O - 65 - 3 13
2. Portland Cements and Concretes

The number of portland cements of the various

types and the areas from which they were procured

have previously been presented, together with the

test methods used for chemical analyses and for determining the water requirements of the neat

pastes and mortars [6]. Also presented in the

first section in this publication were the descriptions of the aggregates and the proportions of the

concretes, together with the mixing procedures and

specification methods used for determining slump

and air content. The cements in this investigation were classified as AE or NAE on the basis of the air contents

of the 1 : 4 mortars in effect at the time the tests were made.^

3. Statistical Treatment of Data

The data obtained for the water requirements

for the different cements were treated statistically as presented in the first section of this publication

[6]. Briefiy this consisted of computing multivariable regression equations to indicate the

relationships between dependent and commonly

determined independent variables as well as the

minor constituents and trace elements. Various

statistical techniques as previously described [6] were used to determine the independent variables

involved. Equations of special significance to the water demands are presented together with

calculated ranges of contributions of the various

independent variables of selected equations. Some

of the limitations of the statistical methods as applied to these studies have previously been

discussed [6]. Equations were computed for the AE +NAE

and for the NAE cements. Other equations were also computed for cements with less than

7.0 percent air as determined by the 1:4 mortar

test, and for cements having 7.0 percent or more

air when determined by this test.

4. Results of Tests

4.1. Chemical Analysis and Fineness of

Portland Cements

The frequency distributions of the cements with

respect to chemical composition, calculated potential compound composition, and fineness as determined by the air permeability method and

the Wagner turbidimeter are presented in table

2-1. In most instances, a considerable range of oxide composition is indicated. This was also true for the calculated compound composition

values and for the fineness values as determined

by the two methods.

4.2. Water Requirements of Neat Portland

Cement Pastes

In table 2-2 are presented the frequency dis- tributions of the cements with respect to the

amount of water used for normal consistency of the

neat cement pastes. The average percentage

water used for normal consistency was 24.70 for the group AE+NAE cements, 24.67 for the group

NAE cements by themselves, and 25.12 for the 12 AE cements. The standard deviation for both

the AE+NAE and NAE cements was 1.494. Presented in table 2-3 are relationships of

various independent variables to the amount of water used with these pastes.* Equation 1, computed for the AE+NAE cements using four of the commonly determined variables, has an S.D.

of 1.149. Equation 2 shows the result of adding,

to the set of the original four variables, five of the

minor or trace elements shown by the high-low and

middle-ends comparisons to be associated with

water requirement. The reduction of the S.D.

from 1.149 to 1.045 is highly significant, as shown

by the "F" test in table 2-22. Using the independent variables of eq (2) and computirig the

relationship for the "odds" and "evens" in the

array of cements, the coefficients of eqs (2A) and

(2B) in table 2-3 were obtained. (See Statistical

Treatment of the Data [6].) When the equations were computed for only

the NAE cements using the same four commonly

determined variables, the relationship indicated

in eq (3) of table 2-3 was obtained. Inclusion

of the minor and trace elements again produced a

significantly lower S.D. value as indicated in eq

(4). (See also table 2-22.) Computing with the

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

resulted in eqs (4A) and (4B). The reasons for some of the anomalies in the "odds" and "evens"

have previously been discussed [6]. In eqs (5), (6), (9), and (10) the A/F ratio was

used instead of the percentage of AI2O3, and in

' The upper speciflcation limit for air content of NAE cements was origi- nally set in early specifications at 8.0 percent in the 1:4 mortar and in later specifications it was raised to 12.0 percent. The specification limits for air content of the AE cements in the early specifications were 12 to 20 percent, then 18±3 percent (in effect at the time these tests were made), and later raised to 19±3 percent. Two cements having air contents in the 12 to 1.5 percent range when tested in the VA mortar were included with the NAE

CSITlGIltS.

* The equations in this and other tables in this section were selected from more than 1,000 trial equations on the basis of interest and relevancy to the

study. See first section of this paper [6] for nomenclature.

14

A
eqs (7), (8), (11), and (12) the C3A values were

used instead of the AI2O3. When the A/F ratio or the C3A were used as variables other changes

such as the use of CaO or C3S as independent

variables were found necessary in order to attain

the lower S.D. values. The S.D. values for both

the AE+NAE and the NAE cements were not

greatly different from those where the AI2O3 was

used in the equations. In each instance the addition of certain minor constituents or trace elements

resulted in significantly lower S.D. values than

when only the commonly determined variables were used (table 2-22).

Regularly conducted interlaboratory tests on

another series of cements over a period of two

years by the five laboratories that made tests in the present study indicated a characteristic standard deviation of 0.66 percent for water used for normal consistency of neat pastes. The values

for S.D. obtained in the present study were considerably higher, indicating that some further source of variation (possibly the wide variety, or some false setting cements, for instance) was

present in these tests Using approximate ranges of values of the independent variables presented in table 2-1 and the

coefficients of eq (2) of table 2-3, the calculated

contributions to the amounts of water used for normal consistency of the neat cement pastes, Wi

,

are presented in table 2-4. Also presented in this

table are the ranges of the computed values.

These computations assume that for changes in each of the independent variables, all of the other

variables are held constant.

4.3. Water Requirements of 1 : 2.75 Cement to

Graded Ottawa Sand Mortars

The frequency distribution of the different ce- ments with respect to the percentage water used

for the 1 :2.75 cement to graded Ottawa sand mortars of standard consistency is presented in table

2-5. There was a considerable overall range of

values for the different cements. There was also an overlapping of the water requirements for the

different types of cement, although the air-entraining cements tended to occur in the lower part of the

distribution curve whereas the highest values were

obtained with some of the type I cements.

The average amount of water used for standard

consistency was 48.24 percent when the AE+NAE

cements were considered, 48.39 percent when

only the NAE cements were considered, and 46.16

for the 12 AE cements. The respective values

for standard deviation were 1.402 and 1.281 per- cent for the AE+NAE and NAE cements.

The air contents of the 1: 2.75 mortars were not

determined, and it was therefore necessary to use

the air-content values of the 1 : 4 cement to standard Ottawa sand mortars normally used in the

air-entrainment test, in computing the equations

for the relationship between various independent

Table 2-1. Frequency distribution of cements with respect to chemical composition and fineness

Variable

SiOj Range, %

19.0 to

19.5

19.5 to 20.020.0

to 20.5

20.5

to

21.0

21.0

to 21.5

21.5

to 22.0

22.0

to 22.5

22.5

to 23.0

23.0

to 23.5

23.5

to 24.0

24.0

to 24.5

24.5

to 25.0

25.0

to 25.5 No. of cts. 4 6 20 26 31 33 22 24 13 6 7 5 2

AI2O3 Range, %

2.5

to3.0

3.0

to3.5

3.5

to

4.0

4.0

to4.5

4.5

to

5.0

5.0

to

5. 5

5.5

to

6.0

6.0

to6.5

6.5 to

7.0

7.0

to7.5

7.5

to

8.0 No. of cts. 4 7 6 30 38 33 30 32 8 10 1

FejOs Range, %

0

to0.5

0.5

to

1.0

1.0 to

1.5

1.5 to

2.0

2.0

to2.5

2.5

to3.0

3.0

to3.5

3.5

to4.0

4.0

to4.5

4.5

to

5.0

5.0

to5.5 No. of cts. 3 1 5 27 48 52 34 15 12 2

CaO

Range, %

60.0

to 60.5

60.5

to 61.0

61.0

to 61.5

61.5

to 62.0

62.0

to 62.5

62.5

to 63.0

63.0

to 63.5

63.5

to 64.0

64.0

to 64.5

64.5

to 65.0

65.0

to 65.5

65.5

to 66.0

66.0

to 66.5

66.5 to

67.0

67.0 to

67.5 No. of cts. 1 3 4 14 26 43 27 26 25 13 7 6 3 1

MgO

Range, %

0

to0.5

0.5

to

1.0

1.0 to

1.5

1. 5 to2.02.0

to2.5

2.5 to

3.0

3.0

to3.5

3.5

to4.0

4.0

to

4.5

4.5

to

5.0 No. of cts. 3 20 41 34 9 21 21 23 19 8

SO3

Range, %

1.2 to

1.4

1.4

to

1.6

1.6 to

1.8

1.8

to2.0

2.0

to2.2

2.2

to2.4

2.4 to2.62.6

to2.8

2.8

to3.0

3.0

to3.2

3.2

to

3.4

3.4

to3.6 No. of cts. 5 33 43 43 27 28 11 5 3 1

LfOss on

ignition Range, %

0.3

to0.6

0.6

to0.9

0.9

to

1.2

1.2 to

1. 5

1.5

to

1.8

1.8

to

2.

1

2.

1

to2.4

2.4

to2.7

2.7

to3.0

3.0

to3.3

3.3

to3.6 No. of cts. 2 49 58 26 33 12 11 3 3 1 1

Insoluble

residue Range, %

0

to

0.1

0.1 to0.2

0.2

to0.3

0.3

to0.4

0.4

to0.5

0. 5 to0.60.6

to0.7

0.7

to0.8

0.8

to0.9

0.9

to

1.0

1.0 to

1.

1

No. of cts. 19 60 64 30 17 3 2 1 2 1

15
Table 2-1. and fineness—Continued

Variable Range, %

1 to

2

2

to

3

3

to4

4to

5

5to6g

to

7

7to

8

g

to9

9to

10

10to

11 to12

12

to

13

13to

14

14

to15 Mr> i> U. nfUi pf^ Uto. 2 I g 5 16 32 22 17 16 12 25 16 16 g

CjS

Range, %

20

to25

25to3030

to35

35

to40

40

to45

45

to

50

50

to55

55

to60

60

to65

65

to70 No. of cts. 33 48 29 C0

C2S

Range, %

5to

10

10to

15

15to

20

20

to

25

25to

30

30

to35

35

to40

40

to45

45

to50

3 14 27 43 68 37 \l 2

C4AF

Range, %

1 to

2

4to

5

5to

6 to

7

y

to

8

g

to

9

9to

10

10

to

11 to12

12to

13

13to

14

14

to

15

15

to

16

16

to

17

J. 'I U> Ul l^/Lo 3 ]^ 3 9 20 32 39 29 30 g \

A/F

S/(A+F)

Range, ratio

0- 6to

0. 9

0. 9

to

1. 2

1. 2to

1. 5

1. 5

ito

1.

8

1.

8

to

2.

1

2.

1

to

2.

4

2. 4to

2. 7

2. 7to

3.

0

3.

0

to

3. 3

3. 3to

3 Q

3. 6

to

3. 9

3.

9

to

4. 2

4 2

to

4 5

4. 5 to

4_ No. of cts.* 4 33 46 31 25 20 22 10 3 1 1 No of rt"! •

I 16 43 58 39 15 10 g 5

C/S** Range, ratio

2 4

to 2.5

2 5to 2.62 6to 2.72 7to 2.82 8

to 2.9

2 9

to 3.0

3 0

to

3.

1

3-

1

to3.2

3 2 to3.3

IN U. Ul Otb. 3 3 17 0/ 45 1 ^

C/(S+A+F)*"

Range, ratio 0 SOto

0. 82

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

IN U> Ul L/tOi 2 3 31 44 41 32 20 14

Fineness AP

Method

Range, cm^/g

2500

to 3000

3000

to 3500

3500

to 4000

4000

to 4500

4500

to 5000

5000

to 5500

5500

to 6000 ^Tn nf ri^Q IN U. Ul Uto. 9 126 40 •J 13 3 2

Fineness Wagner

Turbidimeter Range cm^/g

1200

to

1400

1400

to 1600

1600

to 1800

1800

to 2000

2000

to 2200

2200

to 2400

2400

to 2600

2600

to 2800

2800

to 3000 No. of cts. 1 15 64 64 16 11 6 1 1

*Does not include 3 white Portland cements. '*CaO corrected for amount combined with SO3. •**CaO/(2.8 Si02+1.18 AI2O3+O.65 FezOs), CaO corrected for amount combined with SO3 but not corrected for free lime. Table 2-2. Frequency distribution of cements with respect

to water used for normal consistency of neat cements

Percentage water used for normal consistency

21 22 23 24 25 26 27 28 29 30 31 Type cement to to to to to to to to to to to Total

22 23 24 25 26 27 28 29 30 31 32

Number of cements

I 1 15

1 22

30

4

21

262

14

2

1

10 "3"

82

868

3

20

3

15

IA.__ 1 II 1 6 1

19

1

IIA in 1 1 4 2

1

1

1

1 IIIA_ IV and V. 2 6 3 3 1

Total 1 9 45 59 48 18 4 12 2 1 199

variables and the water requirements of the 1: 2.75 mortars. Plots of air-content values of another

series of cements, studied in a previous investigation [5] indicated that there was a relationship

between the air contents of the two types of mortars. In table 2-6 are presented equations indicating

the effect of different independent variables on

the percentage water used for standard consistency of the 1 : 2.75 mortars. Equations (1) through

(6) were obtained on the AE -|- NAE cements and

eqs (7) through (12) on the NAE cements. Equation 1 was computed from commonly determined

variables, whereas in eq (2), other variables indicated by the high-low test as being significant were included, giving a significantly reduced S.D.

value (table 2-22). Use of AI2O3 alone resulted

in lower S.D. values than when the related variables, A/F or C3A, were used, as may be noted

by comparing eqs (1) with (3) and (5), or (2) with

(4) and (6). In each instance, the addition of minor or trace elements resulted in slightly lower

S.D. values than when they were not used (table

2-22).

. Using the high-low comparison test previously

described it was noted that with the deviations

from eq (2), the for the difference between means of the "high 20" and "low 20" was in the 5 percent range for air-permeabUity fineness and in the 20 percent range for Zn. When used with the

other independent variables of eq (2) the Zn had a

coefficient which was not significant, and the coefficient for the fineness was —0.00030 with an

16
0> >A —400

rH O r-l

00 »0 Tt* <£>•-< !> O CO 00 0>

00 M <o

CO a>

CO •-I

'J' CO o o

eo 00 r- o o o o

ON 1-1 CO

UO CO iC Tji N .-I CO .-•

I I ^

iH 00 OS »C t-- 05 IC 00 Tt* t-- OO

Tt* 00 t'- CO lO O O O O .-( o

O so GO coco coo t-- Tj< (N (M r-c3s ao -^05 coco

ooco t^c^ >-« TP coco r-co

eo Oi CO

rP O O CO O 00

t— CO rH lO CO o o O O .-H o o o oo O O .-HO oo

tot- O h-co lOco

oi t- CO r— OS o lo .-(

1-H O O 1-H 1-t .-H O O O O o o +^ o o o o o o o o

CO if5 C4 00 Tt< »o i-H 00 coo oco CO CO OS O OS lO t- CO coos I—t O lO iC I-H CO

<N O coo CO i-H CN .-H MO CO rH CO .-H CO i-H o o o o oo

.-H O .-H O -H C o o o o —

I o .-H r- o o -- -'C^ (M coco HO T-H O -HO •-'

O

30 OQ oo oo OO oo oo

OO O O OO o o o o o o oo o o

O 00

IL II

CM eo

I

II II

CO CI

t- CO CO 2S

to iC

lO O 2!O CO

to f-- +^

II II

lO +^

II II

N lO +^

II II

N t- +~-'

II II ©"d

X) m

cu

M I

^(5

II II d Q

CO oi

CO

1^

CO

I <Mwm

<;

21 S 52

S5S 7^

cd ci

c4 o

I ^

OS «o

OS OS

OS OS SCO

oc>

CD M

w o

I ^

to M

(N O

00 00

I

COoo

0§CO o o o o o o

00 OS eo eo

CD (N !> CO O O O CO

CO W CO OS

00 CO »0 CO o c5 o o

o o

OS CO

CM —

(

o o o o

CO .-H o o

o c5

C31 TP

(M .-H oo

oo o o oo oo

o o

o o oo woCO o o o

00 CO

TP .-H d d

CO CO

to

Tt< ,-H do

TP CO 00

TP rH 1-H do o o

TP OS CD OS i-H I-H OS COO COOS I-H (M OS O C,-, ^ COrH COM COi-H COM COi-H COM MM 1-H O .-HO rH O .-HO .-HO rH q .-HO oa oo oo oo oo o (-5 oo Oo oo o^ oo oo oo Oo ci>o dd do dd oo dd dd d^J do +° +- +- +- +- +- +° +°

m" om coco O^ O .-h M r- coo ic-H r>. os o M ooco oooo orOS *o irf tod tod os o6 uo cod d +^ +^ ^„ +^

II II II II II II II II II II II II II II II II

fe"^! fe'^! fe'o fe'^ fe'o fe'o

IZJ

qq

o r-T eo

a a

17
Table 2-4. Calculated contribution of independent vari- ables to the amount of water used for neat cement pastes

of normal consistency

Indep6n(i6nt

variable

Valu6s used for

lllUcpcllUtllil, variable

Range of indeVariableuoemcients pneq (9^ haulxi ^ 0

calculated

to Wi

Calculo+oH

ul l/Ull I. to Wl

Arr oUUUw oouu .i5U0 1 A o +n _1_7 0 O. 0

cni2/g. AI2O3--. 3.0 to .5 % 4.5 0.307 +0.9 to +2.3 1.4 CaO 61 to 67 % 6 0.230 +14.0 to +15.4 1.4 SO3 1.4 to 3.0 % 1.6 0.776 +1.1 to +2.3 1.2 Alk 0 to 1.2 % 1.2 0. 546 Oto +0.7 0.7 Cu 0 to 0.05% 0.05 -33.8 Oto -1.7 1.7 P 0 to 0.5 % 0.5 -2.68 Oto -1.3 1.3 Zr _ 0 to 0.5 % 0.5 6.62 Oto +3.3 3.3 SrO 0 to 0.35% 0. 35 -1.54 Oto -0.5 0.5

Table 2-5. Frequency distribution of cements with respect

to water used for standard consistency, 1:2.75 cement

to graded Ottawa sand mortar

Percentage water used for standard consistency

Type 44 45 46 47 48 49 50 51 62 53 64 56 cement to to to to to to to to to to to to Total

45 46 47 48 49 50 51 52 53 54 55 56

Number of cements I 18 '19"17

3821513 9 1 1 1 1 828683203

15

lA ._ 1 11212 4

II 13 11 9

11

A

III...- 5 4 1 1 IIIA 1 IV and V 2 3 4 1 3 2

Total- . 2 7 20 48 64 29 22 4 1 1 1 199

s.d. value of 0.00020. The S.D. value was 1.143

when using the fineness values with the AE -t- NAE

cements. When these two variables were used

with the NAE cements, neither was significant.

With the NAE cements (table 2-6) the three

eqs (7), (9), and (11) use the same commonly determined variables as are used in corresponding

eqs (1), (3), and (5) of table 2-6. Here again the

lowest S.D. of the three was obtained with AI2O

as one of the independent variables (eq (7)), al- though the S.D. values with the A/F ratio and

C3A are only slightly higher. Including the minor

constituents and trace elements in eqs (8), (10),

and (12) resulted in lower S.D. values than in the

corresponding eqs (7), (9), and (11) where they

were not included.

In the previously mentioned interlaboratory

tests, using

a different series of cements, the

standard deviation value of 1.17 was obtained for the percentage water used for standard consistency

of the 1:2.75 mortars made of 44 cements. The

S.D. values presented in table 2-6 compare reason- ably well with this value.

Using approximate ranges of values of independent variables from those presented in table

2-1 and the coefficients of eq (2) of table 2-6, the

calculated contributions to the amount of water

used for standard consistency of the 1 : 2.75 cement

gssosoI a<

(N ^ ^ r-lM

W

lO 00

.-H +"-'

COOS

1-H CO

O l-H

01 I

+^N l-H +^

to CO

fO Oi

O

O +'^

CO CO

l-H CO o ^ 00I ^

t>- 00 00+^ 00+^

f-« 00

1-H

O o o +-

10 o>

CO t~- 00 (N00

1-H

O

00 o 01 00 00 o o +^ o o o o +^ +

+-'

CO "5CO Oi CO 00

+1.

83

(0.

68) CO Tt< COw 0 +-

00 1-H CO ^ +" *+0.

64

(0.

99)

4-1.

93

(0.

69)

+1.

34

(0.

75) 00 OS

00 CO

1-H 0 +- l-H 0 +^ 0 00

CO c3

OS00

00

»0 CO 0 OS

00 OS

f-H

CD OS

OS 00

CM .-H ).

664 ).

207) ^ o

+- o o+"

1-H

O o o +~- 00+^ o o

+" o o

00 1-H 00

t-H CO 00 CO

1-H

O 1-HO 00 O C5 +^ +- o o +^

CO OS

CO

1-H o<=)

CO 00

CD iC

10 1-H o o

00 1-t o o +"

S5 c5 OS CO 10 C-l +

tl II o 10 + +

»n (D

II II

1/5 00^ CO o t-00

i-hqj OSoa M'^o oOos

CD o O r-I

O +^ +^ +^ +^

^a; ^•q ^•a

w+

18

-1
M +

S.D.

1.210 1.116 1.045 0.989 1.214 1.115 1.215 1.116

J2

Oh

+21.9

(14.5) +21.1(16.6)

+227. 4

(45.

7)

+21.9

(14.4) +26.0(14.5)

SrO

-i.28 (1.

22)

-4.

55

(1.

73)

+3.42

(1.63)

-1.22 (1.20)

3

+121.9 (32.

0)

+106.8

(52.3)

+161.3 (41.

0)

+132.

6

(31.

0) +

121.0 (31.9)

3o

+21.6

(11.2) +31.4 (15.

7)

*-6.4 (16.

0)

+20.9 (U.O)+21.4

(11.1)

OS

CO CM O (M 0>fO CO CO CO

00 f-H 00 CO

>0 00 CO o Tf* (M CO CO o o +^ o o +^ oo oo oo oo +^ +^ +^ +^

i-i 00 O COM CD CO o o +"-' o o +^ o o o o +^

0 oo CD I 01 (N oo O O t-H o

cJ o o cJ +--' +~-'

r-I O

1-t CO 00

.-J .-3 o o 1-H o O O 1-H o

(M CO O

1-H O +^

c» Oi r -

C-i r-^ 1-H O ^ O +^ I - +^

to CD O

o c5 1-H o +- +-

00 TP

TP OS

1-t <N +^

CO CO

QO

00 Tp o o

C^eO C^»0 QOuti i-HCJ coco Or- CO lo coos CO OO os .—

i

O CD 00 CD -tp 1-H CO t-H CO tM o o o o o o +- o o

o r-

(N CO

1-1 o

c> o +^

00 O rji ID r, o CO

UO 1-H 00 1-H o o o c5 +~-' +'~^

<M CO

IC 1-H CM M

00 TjH 00O (M

o o +"

TP CO d d +"

ID CN oo CO

eg CO

o 1-H OS coo CO 00 -rt^iO -^00 O r- iCOO CDiO CDO cDO (NO oo oo i-i O oo

o o o o

+

II (I

to 00 OS 00 ^ t00 CO

-h

II II

CO i-H CO ^ lO o TP ^

+

o TP+

II II

lO o +

^o

d d +-'

o o

o o

o o +-

o o +-

II II ^4

to graded Ottawa sand mortars, W2, are presented

in table 2-7. Also presented in this table are the

ranges of the computed values.

4.4. Water Requirements for 1:4 Cement

Standard Ottawa Sand Mortars

to

The frequency distribution of the cements with

respect to air content of 1:4 mortars of standard

consistency is presented in table 2-8, and the

frequency distribution with respect to the amount

of water used for these mortars is presented in table 2-9. The difference in water requirements

of the air-entraining and the non-air-entraining

cements is more pronounced in table 2-9 than in

tables 2-2 and 2-5.

The average amount of water used was 70.40

percent when both the AE and NAE cements

were considered, 71.31 percent when computed for the NAE cements 5 and 57.66 for the 12 AE ce- ments. The standard deviation of the AE-f

NAE cements was 3.989 and for the NAE cements

it was 2.091.

Table 2-7. Calculated contribution of independent vari- ables to the amount of water used for 1:2.75 mortars of standard consistency and the calculated ranges of such

contributions

Range of Coefficients Calculated con- Calculated Independent variable from eq (2) tribution to W2 range of variable (percent) of table 2-6 contribution to Wi

const. =40.40 Air content 1:4 Mortar 1 to 24 -0. 157 -0.2 to -3.8 3.6 AI2O3-.- 2, 5 to 7.5 0.801 +2. 0 to +6. 0 4.0 S/(A+F) l.Sto 4.2 1.30 +2. 3 to +5. 5 3.2 NazO 0 to 0.7 1.33 +0 to +0. 9 0.9

Insol. res 0 to 1.0 -0. 973 0 to -1.0 1.0 MgO 0 to 5.0 0. 135 0 to +0.

7

0. 7 SO3- 1.4 to 3.0 0. 551 +0.7 to +1.7 1.0 Cu 0 to 0.05 19.3 0 to +1.0 1.0 Li 0 to 0.02 111.7 0 to +2.

2

2.2 SrO 0 to 0.35 -2.08 0 to -0.

7

0.7 Pb 0 to 0.05 24.5 0 to +1.2 1.2

Table 2-8. Frequency distribution of the cements with

respect to air content in 1:4 mortars of standard consistency

Percentage air content of 1:4 (cement to standard Ottawa sand) mortar

Type cement 1 4 7 10 13 16 19 21 24 27 Total

to to to to to to to to to to 4 7 10 13 16 19 21 24 27 30

Number of cements

I - 37 41 3 1 82 lA 2 5 1 8

II 1 36 25 5 1 68

IIA 1 1 1 3 III.—. 11 7 2 20 IIIA 1 2 3 IV and V 1 9 4 1 15

Total 2 93 77 11 4 5 5 1 1 199

» The overall average was affected so slightly by the AE cements (which had an average of less than 60 percent) because there were so few of them.

19
Table 2-9. Frequency distribution of the cements with

respect to water used for standard consistency of 1:4 cement

to standard Ottawa sand mortars

Percentage water used for standard consistency

Type 64 66 68 60 62 64 66 68 70 72 74 76 cement to to to to to to to to to to to to Total

56 58 60 62 64 66 68 70 72 74 76 78

Number of cements

I - 1 43 26 7 5 82

867

320

314

lA 1 4 3

11 2 4 35 18 8

11A 1 1

1

1

1 111 1 3 10 2 3 lllA 1 1 IV and V 1 2 10 1

Total.. 2 5 1 6 1 1 6 5 90 56 19 5 197

The equations indicating the relationship of the

various independent variables with the water used

for the 1:4 mortars of standard consistency of

these cements are presented in table 2-10. Equations (1) through (7) were obtained for the AE

plus the NAE cements and eqs. (8) through (14)

for the NAE cements.

Considering the AE+NAE cements, the rela- tionship of the amount of water used to the per- centage air entrained is presented in eq (1) of

table 2-10. The S.D. value of 1.984 is considerably smaller than that of 3.989 (presented in Note 1 of this table) which was computed from

the observed values of the water requirements of

the different cements.

By including seven other commonly determined

variables in the computations as in eq (2), a

significantly lower S.D. value was attained

(table 2-22) as was also the case in eqs (4) and (6)

where the A/F ratio and the C3A, respectively, were used instead of the AI2O3.

By use of certain of the trace elements indicated by the high-low comparison as being significant, further reductions of the S.D. values were

obtained as may be noted by comparing eq (2)

with (3), (4) with (5), or (6) with (7).

Consideration of only the NAE cements resulted

in the eqs (8) through (14) of table 2-10. With

these cements, inclusion of the air content of the

1:4 mortars also reduced the S.D. value as indicated in eq (8), and inclusion of other commonly

determined variables reduced the S.D. value stUl further as indicated in eqs (9), (11), and (13).

(See also table 2-22.) Using the A/F ratio (eq

(11)) did not reduce the S.D. value as much as the use of C3A or AI2O3 values (eqs (9) and (13)),

respectively. By use of certain trace elements

in the computations the S.D. values were reduced

further as may be noted by comparing eqs (9) with (10), (11) with (12), and (13) with (14) (also

table 2-22).

Comparing eqs (1) through (7) with eqs (8) through (14) (table 2-10) it may be noted that

coefficients for the air content are greater in magnitude for the AE+NAE cements than for the

NAE cements alone. Also, NazO and Zr are

OS

CO

f-i id

00 CD O 00 O t-^ 06 + + +

"3 00

00 O iC + +

CO <-i iC 0> 00 u

CO ^" CO --I MlCOtJi CD ID 00 ^ OS CO

M 0>

00 l>- 00' ID CO i-l

01 CO

CO

O 00

oi

CO ^

10 01 ^ o

I ^

kD CO o o o

1-i '^O OSCO 01 010

(M coco CD CO coco 00 00 00 00

lO CO

lO IN o o

CO CO o o _ _ 00 00 00

CD

!N o o oo

d d

O CD

ID O ^ CO

CM O ^

IN OS OS O

Tj- ID »0

IN O

(M OS 00 CO 00 CD I-l Tt< CO (N 00 i-t tN OS 1—1 OS 00 CD OS C-J CO ^ O

o o

4-^ 00 00 00 +^ +'-' 00 00 o o

OS

tH CO

10 1-1 CD CD O i-H O 00 CO !>

CO 10 1* >0 (N 00 CO ^ o f-i O NO o o 00 00 O

o o o o

(N OS (N d d d d

00 CO

(N CO o o

00

OS C<) d d

(N CO O CM O CO >-» .-H TP CO »D CO .-Id d d

00 O CO o (M ID

OS O OS O

Tfi CD »0 CO

OS O O OS 001 ^o

ID O Oh- 1-^0 O CD

10 TfH COCO »D Tt* coco OsO OSO OSO OSO

t- o +

II II

iD

^6 +

II II

CO CO + +

Jl". + + + +

fe'^ te"^ ^V. fe-"

1-1 <N

20
CO M o >-<

r-i »h' CO C^* O O

d

0> 1-H rH CI + +-

CO 00 CD i-H

CO i-H

W W3 N to Tf uiui 1-4 CO 00* d W 1-H lO CD (M

CM 00

00

CO t-H

O 00

00 id

oo'

o ^

CO ^

00 C^l 4C »c

-0.

00059

(0.

00029)

-0.

00034

(0.

00028) CN O oC O

°.g

-0.

00050

(0.

00042)

-0.

00067

(0.

00029)

-0.

00048

(0.

00028) ^ 05

SO M o o o

o o -0.

00038

(0.

00027)

0.

546

0.295)

0.318

0.280) 0.247 0.

439) 0.

021) 0.

401

1

0.

561 0.

2961 0.312

0.280) 0.585 0.

294) 0.

369 0.

278)

o o +0.

359

(0.

118) ^ OS oo+^ +0.

509

(0.

164)

+0.

132

(0.

119)

+0.

331

(0.

117) O 00

CO ^ o o +^ +0.

340

(0.

116)

CO 00 W CM o

!> CD

h- CD

tfS (O

OS 1—

1

^ CO oCO o(N CO

CO (N

.-1 00

Oi O iC CO

l-H O i-H O w O o o o o o o +- +

o o

-1 O CM o do d d

do d d

IC C3S iC Ol

IC CM O CO

CO CO 00

00 CM o eo oo r-1 O

CD CO d d

ooo O 00

CD O

o oo

00 1-t »oo CO >-« Olo oo OS 00 CO ooo 1^ oo too COO lo o coo ^6

o o

I ^ oo oo

CM O -^-co lO d CM iC"^ oico CO'-' CO •-' lo <-h cm «-h

II II +

II II + + + + +

fe'^ fe'^' fe'o +

II II

present in eqs (1) through (7) but not in (8)

through (14) where the coef/s.d. ratios for these

variables when tried were less than 1. Including

the trace elements in the computed equations decreased the coef./s.d. ratio of the loss on ignition

to less than one with the AE+NAE cements, but

not with the NAE cements, although the coeffi- cients were reduced to some extent in the latter

case. The coefficients of other variables such as

AI2O3, A/F, C3A, and S/(A+F) were larger with

the use of the trace elements than without them

and the coefficient for APF was smaller in

magnitude.

The S.D. values obtained for the equations in table 2-10 were approximately the same as the

standard deviation value of the water used for standard consistency of the 1 : 4 mortars in the

regularly conducted interlaboratory tests on

another series of cements mentioned previously.

Using approximate ranges of the independent

variables determined from values presented in table

2-1 and the coefficients of eq (3) of table 2-10,

the calculated contributions to the amount of

water required for standard consistency of the 1 : 4

cement to 20-30 Ottawa sand mortars are presented, together with the ranges of such contributions, in table 2-11.

4.5. Concrete Made With a Constant

Water- Cement Ratio

The frequency distribution of the cements with

respect to slump values when concrete was made

with a water-cement ratio of 0.635 is presented in

table 2-12 and the frequency distribution with

respect to the air content of these concretes is presented in table 2-13. The slump values

ranged from 2.0 to 8.5 in. and the air-content

values ranged from 0.5 to 10.5 percent.

Table 2-11. Calculated contribution of independent vari- ables to the amount of water used for 1 : 4 mortars of standard consistency and the calculated ranges of such

contributions

Coefficients Calculated Calculated Independent Range of from eq (3) contribution range of variable variable of table to W3 contribu2-10 tion to W3

Air Content const. =67.7

1:4 Mortar 1 to 24 % -0. 954 -1.0 to -22.9 21.9 AI2O3- ---- 2.6 to 7.5% +0. 918 +2. 3 to +6.9 4.6 S/(A+F) 1.8 to 4.2% +1. 712 +3. 1 to +7. 2 4.1 MgO 0 to 5.0% +0. 399 0 to +2.0 2.0 Na20 0 to 0.770 +2.12 0 to +1.5 1.5 APF-__ 3000 to 6500 -0. 00041 -1.2 to -2.3 1.1

Insol. res 0 to 1.0% -1.72 0 to -1.7 1.7 Cu 0 to 0.06% +66.3 0 to +3.3 3.3 Ti.__. .05 to 1.0% +3. 36 0.2 to +3.4 3.2 v 0 to 0.1% +18.5 0 to +1.8 1.8 Rb 0 to 0.01% +161.6 0 to +1.6 1.6 Zr 0 to 0.6% -4. 81 0 to -2.4 2.4

In figure 2-1 is presented a plot, made by

averaging groups as previously described [6], of the values of slump of the concretes versus the

percentage water used for standard consistency of the 1:2.75 mortars. The value of —13 for the

"quadrant-sum" of this plot would indicate a 98

percent probability of a significant relationship.

The significance of this relationship is probably

21
Table 2-12. Frequency distribution of cements with respect to slump of concrete made with a water cement ratio of 0.636

Slump, inches

Type cement 2.0 to 2.5 to 3.0 to 3.5 to 4.0 to 4.5 to 5.0 to 5.5 to 6.0 to 6.5 to 7.0 to 7.5 to 8.0 to 8.5 to Total

2.5 3.0 3,5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Number of cements

I 9 13 18 12 11 4 3 3 5 2 2 82 lA 1 4 2 1 8

II 1 5 9 15 5 2 4 9 5 6 5 2 68 IIA 1 1 1 3

III 1 5 6 2 2 3 1 20 IIIA 1 1 1 3 IV and V 4 1 1 2 1 1 2 2 1 15

Total - 11 23 37 27 19 9 9 16 12 12 15 7 1 1 199

Table 2-13. Frequency distribution of percentage air in

concretes of water cement ratio of 0.635

Percentage air

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 7.0 9.0 Type cement to to to to to to to to to to to to to

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 7.0 9.0 11.0

Number of cements

I 2 8 15 26 17 11 2 1 lA 7 1 II..._ 1 16 22 16 6 3 1 2 1 IIA 1 2 III 2 8 6 1 2 1 IIIA 1 2 IV and V 2 6 5 2

Totals

.

3 28 51 53 24 18 3 3 1 1 2 U 1

'o ' '

' ~ o

o - o _ o

1 1

o

1 1 1 1

o 0 o o

o

1 1 46.5 470 47.5 48.0 48.5 PERCENTAGE WATER I 2.75 MORTAR

Figure 2-1. Results of plotting 12 pairs of averages of slump of concretes made with a water-cement ratio of 0.635

versus the percentage wa.ter used for the 1:2.75 cement to graded Ottawa sand mortar.

(The ratio of points in opposite quadrants =10/2 and the quadrant sum= — 13 See section 4.1 of section 1 [ref. 6]) Table 2-14. Coefficients of equations relating the slump and air contents of concretes made with a water-cement ratio of 0.635

to various independent variables

Equation Type cements Note Const. A4 As S.D. Avg. AE+NAE.

AE+NAE.

.do...

.do...

.do...

-do...

NAE.

NAE.

_...do....

-...do....

---.do....

-.-.do-...

()

(')

(')

(')

(')

(2)

(2)

(=)

S4 =

S4=+15. 61 s.d.= (1.92) S4=+23. 77 s.d.= (3.84) Sj=+43. 92 s.d.= (1.04) S4= +3.35

s.d.= (0.16) A4 = s.d.=

S4 = S4 = s.d.=

S4 = s.d.=

S4 = s.d.=

S4 = s.d =

A4 = s.d.=

-1.60

(0. 11)

-0.26

(3. 63)

H-13. 81

(4.16)

+49. 22

(1.27)

: +3.14

' (0. 26) -0.331

(0. 178)

-0. 159

(0. 027)

+0. 063

(0. 051)

-0. 400

(0. 080)

-61.8

(1.6) +0. 529

(0.055)

-0. 198

(0. 086)

-69.9

(2.0) +0. 661

(0. 143)

+0. 455

(0.013)

+0. 273

(0. 024)

1.654

1. 527

1.557

0. 564

L367

0. 650

1.478 1.476

1.460

0. 517

1.402

0. 657

4.48

4. 24

' 190 cements.

- 176 cements.

22

A.
.-I i-H O O ^ CO «D OS M Q »-l 00 ^ N C5 M

O OOM r-t 00 TjJ 00 Tji oi t-^ ^ OO CO ^ ^

CO « O O r CO O 00 Ci »o o c»5 oo r

CO 00

I-H r- 00 rft Oi

CS CO M tfi »c

l^50

CO (N

CD 7""

W 1-H

00 00 QOCO

CO CO

82

1050. r

CO N

'-<0--tOOO<-"00000^0^0'-HO^OOOOO^O^O

eDCS50Ni-iTHiCCOO(N«DC^«OC^«DMOWt^c5tDC^r^<

5 CD t- CD M

5 S c5 c5 OOOOrHOOOOOOOOOOOOOOOOOOOOOOO

0000

0000

_ ,1 OJ OS OS 00 C«3^COi-iiOt-C^^ 00000000

00 i-i r-- M

Q o M CO N 0000

IT

0000

»00'OOCDO»00'^0"^0'OOiOOOO'' 0000000000000000000000000000

H-^cofOTt<oiTHas»dc^ooco 4CO"^C»Ci—iTt*^Tj<0'*0*OOiOomO'00'^0'*OiOO'00 +^ +^+^ +- +- +- +-+- +-

<+

enhanced by the fact that the air-entraining

cements had greater slump values and lower

water requirements for standard consistency of the 1 : 2.75 mortars than did the NAE cements.

For example, all of the 14 AE cements are included

in the group of 16 represented by the point at 46.6

percent water and 7.5 percent air in the upper left corner of figure 2-1

.

The average value for slump for the AE+NAE

cements was 4.48 in. with an S.D. value of 1.654. For the NAE cements the average was 4.24 in. with an S.D. value of 1.478. The average for the

12 AE cements was 7.88. In table 2-14 are pre- sented the coefficients of equations expressing the

relationship of the slump values of the 0.635

W/C ratio concrete to the percentages of water

used for standard consistency of the 1 :4 mortars

(W3) and the 1 : 2.75 mortars (W2), and the watercement ratio used for the 5± 1-in. slump concretes

(W5). A high degree of correlation existed between the slump values obtained with the 0.635

W/C ratio concrete and the water used for the

5 ± 1-in. slump concrete (eqs (3) and (8), table

2-14). Slump of the constant-water-cement-ratio

concrete was related significantly to water requirements of the 1:4 or 1:2.75 mortars (W3 and W2,

respectively) except for the case of the 1 : 2.75

mortars with NAE cements (eq (6)). The equations indicating the relationship of the

various independent variables to the slump of the

0.635 W/C concretes are presented in table 2-15.

Comparing eqs (1), (3), and (5) of table 2-15 with

eq (4) of table 2-14 it may be noted that the S.D.

values were lower when certain commonly determined variables were included with the air content of the concrete in solving the equations.

This was also true for the NAE cements, eqs (7),

(9), and (11) of table 15, as compared with eq (9) of table 2-14. Inclusion of the elements Ba, Co,

and Pb present in minor quantities in the cements

significantly reduced the S.D. values of the equations in each instance (table 2-22) . The effect of using the "odd" and "even" cements is indicated

in eqs (2A) and (2B) in table 2-15.

Again using the approximate ranges of the in- dependent variables obtained from values pre- sented in table 2-1 and the coefficients presented in eq (2) of table 2-15 the calculated contributions to the slump of the 0.635 W/C ratio concretes to- gether with the ranges of such contributions are presented in table 2-16. The coefficient for Pb

in eq (2A) is negative, while in eqs (2) and (2B) it

is positive, and in all three cases the coefficient is significantly larger than its S.D. value. The

reason for this discrepancy is that there were

only 31 finite values of Pb, the rest being below

the reporting limit and being recorded as zero. The split of finite values between the odds and

evens was by chance not uniform and therefore

did not produce results in agreement with eq

(2) calculated from the total number.

Concretes made with 29 of the cements used in

this program of tests had slump values in the

23
Table 2-16. Calculated contribution of independent

variables to the slump of concrete made with a water- cement ratio of 0.635 and the calculated ranges of such

contributions

Independent

variable

Range of variable

(percent)

Coenicients from

eq. (2; of table 2-15

Calculated

contribution

to S4

Calculated range of contribution to S4

const. =6.48 Air in concrete. 0 to 10 +0. 587 0 to +5.

9

5.9 AI2O3 2.5 to 7.6 -0. 524 -1.3 to -3.9 2.6 Fe203 1.0 to 6.0 +0. 398 +0. 4 to +2. 0 1.6 SO3 1.4 to 3.0 -0. 676 -0.9 to -2.0 1.

1

K2O 0 to 1.

1

+1.12 0 to +1.2 1.2 Ba 0 to 0.20 +4. 13 0 to +0.

8

0.8 Co 0 to 0.01 -151.3 0 to -1.5 1.6 Pb 0 to 0.05 +28.0 0 to +1.4 1.4

5±l-m. range in the first series of concretes,

which had a constant water-cement ratio of 0.635

and also had the same W/C ratio in the second

series. The duplicate batches of concrete made

from these cements for the second series of concrete tests thus afford a means for evaluating the

reproducibility of the slump values and the air- content values. The standard deviation computed from the 29 pairs of slump values was 0.46

which was significantly smaller than the S.D.

values presented in table 2-15. The pairs of values

of each of the cements were usually determined the same day and with sand and gravel from the same

shipments, whereas the making of concretes from

a majority of the different cements was made

during a period of 2 years, with only a few concretes made 3 and 4 years from the start of the

test series. A number of shipments of sand and

gravel were obtained in this period.

The air-content values of the 29 pairs of deterTable 2-17. Frequency distribution of water cement ratios required for concrete with 5±1 in. slump

Water cement ratio

Type cement

0.550 to

0.575

0.575 to

0.600

0.600 to

0.625

0.625 to

0.650

0.650 to

0.675

0.675 to

0.700

0.700 to

0.725 Total

Number of cements

I 5 32 34 7 1 79 lA 4 4 8 n 15 29 22 i 67 IIA 1 1 1 m 2 6 11 1 20 niA 2 1 3 IV and V 6 6 3 15

Total._. 5 7 30 73 70 9 1 195

UJ

o

1 1 1

1

0

1

-1- 0 _

0

00 - 0

c - 0 +

0 1 1 1 1

0

1 ^ S ''e.O 465 47.0 475 48.0 48.9 PERCENTAGE WATER 12.75 MORTAR

Figure 2-2. Results of plotting 12 pairs of averages of water-cement ratio used for concretes having a 5± 1-inch slump versus the percentage water used for the 1:2.76 cement to graded Ottawa sand mortar.

(The ratio of points in opposite quadrants=10/2 and the quadrant sum =

+16. See section 4.1 of section 1 [ref. fi])

DEPENDENT

VARIABLE INDEPENDENT VARIABLES

WATER

REQUIREMENTS NO2O S A + F

AIR P. FINE WAGN.

FINE

ALL

CEMENTS

(I)

(2)

(3) (4) NO +7

L?+8

NON-AIRENTRAINING CEMENTS

13)

(4)

NON-AIRENTRAINING CEMENTS, ONE LAB

ONLY

(I)

(2)

(3)

(4)

\

L?

0

L?+ 15 -5 + e +7 no +24 -7

L?+5

note:

(1) ratio of number of plotted points in pairs of diametrically opposite quadrants.

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

(31 apparent nature of relationship. l= linear, nl non linear , no = no apparent relation l? = nature of relationship not determinable.

(4) quadrant sum in corner test (see ref 6),

Figure 2-3. Results of plotting water-requirements of 1:2.75 cement to graded Ottawa sand mortars on the "Y" axis versus independent variables on the "X" axis. 24
Table 2-18. Frequency distribution of air content of concretes made with sufficient water to obtain a 6±1 in. slump

Air content

Type cement Oto .5 .5 to 1,0 to 1.5 to 2.0 to 2.5 to 3.0 to 3,5 to 4.0 to 4.5 to 5.0 to 7.0 to 9.0 to 11.0 to 13.0 to Total

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 7.0 9.0 11.0 13.0 15.0

Number of cements

I 6 12 18 17 14 9 2 1 97 lA 1 3 3 1 8

II 6 19 16 16 3 6 1 1 67

11A 1 1 1 3

III 1 5 4 5 2 2 1 20 IIIA .._ 2 1 3 IV and V 2 7 3 1 1 1 15

Total 13 38 44 41 20 12 9 1 2 1 4 5 3 1 1 195

Table 2-19. Coefficients of equations relating the water-cement ratio and air content of concretes of 5± 1-in. slump to various independent variables

Equation Type cements AE+NAE.

AE+NAE_,

-.do_

-.do.

..do_

..do_

NAE_

NAE_

_.d0-.

..do..

..do..

..do..

Note Const.

Ws=

(') W6=+0.425

S.d.= (0.028)

0) W6= +0.320

s.d.= (0.058)

(') W5=+0.675

s.d.= (0.003)

(1) W5=+0.657

s.d.= (0.002) w A6=-2.10

s.d.= (0.15)

(') m W5=+0.737

s.d.= (0.048)

(2) W6=+0.614

s.d.= (0.056)

(') W6=+0.662

s.d.= (0.006)

C) W6=+0.662

s.d.= (0.003) As = -0.693

s.d.= (0.214)

+0. 00303

(0. 00039)

-0. 00131

(0. 00068)

Wz

+0. 00660

(0. 00120)

+0. 00266

(0.00115)

A3

-0.0045

(0. 0004)

+0. 505

(0. 016)

-0. 00266

(0. 00083)

+0. 306

(0. 029)

-0. 0091

(0. 0006)

-0. 0123

(0. 0015)

S.D.

0. 02519

0. 02201

0. 02342

0. 01905

0. 01691

0. 826

0. 01981

0. 01965

0. 01957

0. 01930

0. 01678

0. 669

Avg.

0. 6385

0. 6430

1 190 Cements. 2 176 Cements.

minations had an estimated standard deviation

of 0.17. The regression line indicating the relationship

between the slump of the constant water-cement

ratio concrete to the water-cement ratio used for

the 5±l-in. slump concrete (eq (3), table 2-14),

had an S.D. value of 0.56 which compared reason- ably well with the 0.46 value previously mentioned.

4.6. Concretes With a Slump of 5±1 Inches

The frequency distribution of the cements with

respect to the water-cement ratio used to produce

a concrete with 5±1 in. slump is presented in table 2-17 and the frequency distribution with

respect to the air content of these concretes is presented in table 2-18. The water-cement

ratios ranged from 0.550 to more than 0.700 and

the air content ranged from less than 0.5 to more

than 13.0 percent.

In figure 2-2 is presented a plot of the watercement ratios of the 5 ± 1-in. slump concrete versus the percentage water used for normal

consistency of the 1:2.75 mortars. The "quadrant-sum" value of 15 indicates a high degree of

correlation. The air-entraining cements with the

low water requirements were for the most part

responsible for the point in the lower left corner. In figure 2-3 is presented a summary of the

the results of plotting the amount of water used

for the 1:2.75 mortars versus various independent

variables. The plots for all cements (AE+NAE)

or for the NAE cements based on results obtainecl

from all five laboratories do not (with one ex- ception) indicate any very significant relationships. Using the same technique of plotting and

the results obtained only in the one laboratory

with the greatest number of tests appeared to indicate that cements having high AI2O3, C3A, or A/F ratios also had high water requirements for

the 1 : 2.75 mortar.

25
A similar series of diagrams is presented in figure

2-4 showing a summary of the results of plotting

the amount of water used for the 5± 1-in. slump

concrete versus various independent variables.

These tests were all made in one laboratory. The

air content of the concrete appeared highly significant for both the AE -j- NAE cements and the

NAE cements. For the NAE cements the SiOa,

AI2O3, SO3, C3A, CaS, C2S, and A/F ratio also appeared to have a significant relationship to the

amounts of water used for the concretes. In table 2-19 are presented equations showing

the relationship of the water-cement ratio of the

5 ± 1-in. slump concrete to the percentage water

used for the 1 : 2.75 and 1 :4 mortars (W2 and W3),

the air content of the 1 : 4 mortar (A3), and the air content of the concrete ( A5) . Also presented is the

relationship of the air content of the concrete versus the air content of the 1 : 4 mortars.

Equation 2 and figure 2-2 represent relationships between the same pair of variables. The

apparent contradiction between the linear equation and the curvilinear appearance of the plot is due to peculiarities of these data and is explained more fully in section 1 [6]. Equations 2 and 7 indicate significant relationships between the water requirement of the

constant slump concrete (W5) and the water

requirement of the 1:2.75 mortar for both the

AE +NAE cements and the NAE cements.

Comparing equations (1), (2), (3), and (4), or eqs (6), (7), (8), and (9), it may be noted from

the lower S.D. values that the water requirement

of the concrete showed a more significant rela- tionship with the air content of the concrete (A5)

than with the air content of the 1 : 4 mortar or the water requirements of the 1:4 or 1:2.75

mortars. The relationship of the W/C ratio and

air content of concrete as well as the entrained

air in the concrete versus the W/C of 1 : 4 mortars

has been discussed by Abrams [7]. For both the AE +NAE and the NAE cements

there was a correlation between the air content

of the concrete and the water requirement as indicated by eqs (4) and (9) in table 2-19. A

comparison of eqs (5) and (10) of table 2-19 with

eqs (5) and (10), respectively, of table 2-14 shows

that the relationship between air content of the

concretes made with 5 ± 1-in. slump and air content of the 1 : 4 mortars produced a higher

S.D. value than did the relationship between air content of the concretes made with a constant

water-cement ratio of 0.635 and the same independent variable.

In table 2-20 is given a further set of equations

expressing relationships between W/C ratio for the

constant slump concretes and other sets of independent variables, including some of the minor

constituents. The average and standard deviation values of 0.637 and 0.02454, respectively, for the AE+NAE cements, and of 0.641 and 0.01908

for the NAE cements alone differ slightly from

those in table 2-19. (The average for the 12 AE

cements was 0.582.) This is because all cements
CO 0.

01361

0.01343 0.

01285

0.

01344

0.

01367

0.

01352 0

0.

01338

-0.271 (0.

170)

-0.

262

(0.

236)

-0.

265

(0.

171)

-0.

221

(0.

170)

\o.

73)

+0.97

(0.84) +1.35(1.44) +1.16

(0.74) +1.10(0.73)

am

-(8;g5% *-(Hi) -0.047 (0.

032)

-0.

048

(0.

032)

ii il il il il il il il

oo oo oo oo 03 00 00 00

1

+0.

0095

(0.

0076)

•+0.

0006

(0.

0119)

+0

0110

(0.

0102)

+0.

0115

(0.

0075)

+0.

0111

(0.0075) "'(a

0075)

+0.

0090

(0.

0075)

&<

+0.

0000030

(0.

0000024)

+0.

0000029

(0.

0000024)

il il il il ii il if il

00 00 00 00 00 00 00 00

CD + -0.

00278

(0.

00222)

+0.

0035

(0.

0024)

d

+0.00241 (0.

00038)

+0.

00248

+0.

0108

(0.

0019)

+0

0107

(0.

0019)

-0.

0050

(0.

0014)

-0.

0054

(0.

0014)

-0.

0059

(0.

0020)

-0.

0049

i

+0.

0061

(0.

0012)

+0.

0050

(0.

0012)

+0.

0044

(0.

0017)

+0.

0058

(0.

0017)

ii ii ii il il ii ii il

fs °s <fs °s <fs °s °s °s

Const. si il si si il il II IS

°s °s °s °s °s °s. °s

ii p p ii ii ii ^i

££££££££

w ; : < 1 : Z i 1 H •§ §

<! ; 1 i

4 4

Equations

O) +

1 i i i i i 1

s2 il il

00 00 00

s?g ns s:2 00

§i ii il

00 oe 00

il

^ o +^

§1

OS

So ll go §1 II II II ll

00 00 00 00 00 00 00 00

do do dd ;

; do do dd

i§ i§ ii 38 si si ii si

do do do 00 00 do 00 do

do dd dd dd

°s °s

ii 11

00 =s

il il il il

do do do 00

ii il il il

do do do do

il il ii il il il il il

fS fS =3 °S °S °S fS °S

if ii si si si si ii ii |d |d |d |o |d |d |o |d

i-^ 1^ ii ^i ^i ^i ^i

^ -§ -§

; I : « ^ g

»

27
with missing values for any of the independent

variables shown in table 2-20 were eliminated from

the calculations in developing the equations in table 2-20.

The inclusion of commonly determined properties of the cements as variables (eqs (1), (3), and

(5) of table 2-20) reduced the S.D. value significantly from that obtained when only the air content was included as in eq (4) of table 2-19.

In table 2-21 are presented the calculated contributions of the various independent variables to the water-cement ratio used in preparing the

5±l-in. slump concretes. Although eq (2) did

not have the lowest S.D. value in this series it was

used as the basis for these calculations because of

its conformance with similar previous equations on which these calculations were reported.

4.7. Calculations on HighCements

and Low-Air

One of the problems in dealing with these data

has been the question of how to treat the AE

cements. Since there were only 14 of these out of

the total number of 199, it was not feasible to cal- culate regression equations on the AE cements

alone for more than one or two independent

variables.

One way of dealing with this situation is to treat the cements as all one population, making

calculations on the AE+NAE cements, and then

to repeat the calculations with the AE cements

eliminated, and to observe the effect of this elimination on the calculated coefficients and standard

deviations. This was done throughout this study.

However, cements with high air contents whether

or not so designated by specifications appear as Table 2-21. Calculated contribution of independent

variable to the water-cement ratio used in preparing concretes with a 6±1 inch slump and the calculated ranges of such contributions

Coeffi- Calcucients Calculated lated Independent Range of from contribution range of variable variable eq (2) to Ws contri- (percent) of table bution

2-20 to Ws

const. =0.632

Air in concrete 0 to 13 -0. 0096 0 to -0. 125 0. 125 AI2O3 2.5 to 7.5 +0. 0050 +0. 012 to +0. 038 0. 026 FezOs 1,0 to 5.0 -0. 0054 -0. 005 to -0. 027 0.022 SO3- 1.4 to 3.0 +0.0113 +0. 016 to +0, 034 0. 018 Insol 0 to 1.0 +0. 0095 0 to +0. 010 0. 010 K2O 0 to 1.1 -0. 0135 Oto -0. 015 0. 016 Ba __ 0 to 0.20 -0.043 0 to -0. 009 0. 009 Co 0 to 0.01 +1.14 0 to +0. Oil 0. Oil Pb 0 to 0.05 -0. 271 0 to +0. 014 0. 014

though they belong to a different population with

respect to some of the dependent variables, and some other method of treating this situation was

desired.

Since the specification limit which divides AE

from NAE cements is more or less arbitrary and

has been changed a number of times (see note 3 on page 14), it was felt that using a lower division point for dividing the values into low-air and

high-air might be fruitful. For these data, a value of 7.0 percent air in the 1:4 mortar was

selected, since this was close to the earlier specification limit of 8.0 percent and gave an approximately even split of the data. The group with 7.0 percent

air or higher is referred to as the "high-air" group

and those with less than 7.0 percent as the "low-air"

group.

Separate equations for these two groups were computed for the water requirements for the

1:2.75 and 1:4 mortars, the concretes of 5±l-in.

slump and for the slump of the constant-watercement-ratio concretes. The best of these equations are presented in table 2-23. Independent

variables with a coef./s.d. ratio of less than 1 were

deleted when preliminary trial equations indicated

that they were not significant and the various

exploratory techniques previously described [6] were employed to find additional independent

variables which were then used in fitting each

equation.

Table 2-22. "F" values for significance of reduction of variance due to added variables

Table Equations "F" ratio D.F.

Critical'F" ratio

7=0.01 0.05

2-3 1 and 2 8.31 5, 170 5,170

5,170

3. 12 2. 27

3 and 4 8. 39 3. 12 2. 27 2-3 cont 5 and 6 7. 32 3. 12 2. 27

7 and 8 7.64 6,170 3. 12 2. 27

9 and 10 7. 12 5,158

5,158

4, 166 4,166

5,153 3,155

4,154

7, 171

6, 160

5, 155 5,155

3. 13 2. 27

11 and 12 7.49 3. 13 2. 27 2-6 1 and 2 8. 67

9. 08

3. 44 2.43

5 and 6— 3.44 2.43 2-6 cont 7 and 8 6. 55 3. 13 2. 27

9 and 10 10. 77 3. 91 2.67

11 and 12 8.32 3. 44 2.43

2-10 1 and 2 5. 17 2. 75 2. 06

8 and 9 4. 16 2.92 2. 16 9 and 10 5.86 3. 13 2.27

11 and 12 6.24 3. 13 2. 27

13 and 14 6. 27 5,155 3,173

3, 173

3, 174

3. 13 2. 27 2-15 1 and 2 3. 96 3.83 2.66

3 and 4 3. 52 3.83 2.66

5 and 6 3. 56 3.83 2.66

7 and 8 3.60 3, 161 3.83 2. 66

9 and 10 3. 30 3, 161 3.83 2. 66

11 and 12 3. 25 3, 162 4,156

3,157

3,156

3.83 2. 66 2-20 7 and 8 2. 13 3. 44 2.43

9 and 10 L58 3. 91 2.67

11 and 12 2. 34 3. 91 2. 67

5. Discussion

One of the factors which is undoubtedly

partly responsible for the comparatively poor

correlations between the quantities of water used

for pastes, mortars, and concretes is the leeway

permitted in specifications. A range of 10 in the percentage flow on the flow table, even for any one skilled operator, permits some range in the percentage water used. Another factor is

the nature of the sand which may vary slightly

from batch to batch. The flow tables in different

laboratories may differ slightly even though

calibrated by means of the Cement and Concrete

Reference Laboratory flow table mixture. Differ- ent skilled operators, although trained to follow

specification test methods, may manipulate the

mortars in slightly different manners or time their

28
CO

m4-

rT» ^ I

00 o o

CO

CO o>

•-< o o

lO OS

CD OIM 2 +

O CD CD OS ^ O O

OS T-H OS (M

^

i-H CO 3 Tf (N _ ^ O) 3 CD --"

cooi _«6co 91^^ '-5 3 CO rH W

I w

CO o o w O O O (M

CO CO o o

„ o o O o o

O ic

<N —I

CM CO

rJH O O CD

OS iC) CO CD

. CO i-H

1-1 00

CD CO

00 ^

o o

ttj &Li CO CD

, if5 00 I "5 -f-coco -f-ooic

TP O

I O CO +CN »C

(M iC "CD .-H O CO

CO

00 CO "O o

^ I ^

o o 50 0

OCDCD OOO CO 00 coos

1-H <-H 00 OS oo oo M«DQO c-iOS'-H mCDCO c-5—ICO 5-;d Ood Odd o^o 5+^ 5+^ Odd 5'^

^ (N CD

OS CO "-I CO o o 00 O

' ^od 5+^ Odd 5'^

O «-( (M

•-• o «o Odd 5+^

lO CO

00 .-H t=^ CO(M (MO 1-H r-1 CO »o ^

00 o o

OS (D o o

oQCO--

Const.

=

+3.33

=

(1.11)

Const.

=

+8.22

=

(0.

83)

Const. +0.

647

(0.

015) ^

odd

u+-

II II II II II II li

manipulations differently so that the final flow

value of the mortar, penetration value of the

Vicat needle in the neat paste, or slump value of concrete may not always coincide with values

obtained by other operators.

Because of the leeway permitted in determining

the amount of water used for a paste, mortar, or concrete together with the variability and in- accuracies associated with the test methods and

results as well as the lack of information on certain

variables, the effect of some of the independent

variables may be masked and there will always

be a limit to the degree of fit which can be attained

for any set of variables.

As stated in the introduction, the use of dif- ferent percentages of water in the specification test mortars has been justified on the basis of the rela- tionship to the different water demands of these

cements when used in concrete. However, plotting the individual water-requirement values of

the mortars against those for the concretes made

of the cements in this investigation indicated a

rather poor relationship, especially for the non-airentraining cements. This would appear to justify

the use of a constant water-cement ratio for the

specification compressive strength test mortars.

Different values may be considered for use with

air-entraining and non-air-entraining cements.

The principal variable in determining the water

requirements in the mortars and concretes was the

air content of the mortars and concretes. This

study confirmed that there was a significant rela- tionship between the air contents of the 1 : 4 mortars and the concretes. It has previously been

reported that, for air-entrained concretes, different

cements may require different quantities of air- entraining agents depending to some extent on

their C3A content, in order to obtain the same air content [8]. This present study confirms that the

water requirements of the portland cements are related to the chemical characteristics.

The following portion of the discussion deals

with the computations made on the AE+NAE

and on the NAE cements alone. Based on the equations in the tables and subject to the limitations

previously discussed [6], it appeared that a number

of independent variables were involved. For neat

cement pastes, mortars, and concretes, water re- quirements increased with AI2O3, A/F ratio, or C3A. The use of any of these three independent

variables together with an appropriate group of other variables appeared to have approximately an equal effect on the S.D. values in any one series of equations for the mortars or the concretes. The neat cement pastes which required the greater

amounts of water for normal consistency also had

higher fineness, CaO, and SO3.

In the equations computed for the 1 : 4 mortars,

the coefficient for the effect of fineness was negative whereas for the neat cements of normal consistency it was positive. Fineness of the cement was apparently of no significance in the two

concrete series. With the 1:2.75 mortars the

29
effect of the fineness of the cement was possibly

included to some extent in the air-content values

of the 1 : 4 mortars used as one of the independent

variables for the computations of the 1 : 2.75 mortar

relationships. The use of silica modulus (S/

(A+F)) in the calculations for the 1:4 and 1 : 2.75

mortars resulted in lower S.D. values while the

use of the Fe203 content of the cements resulted in lower S.D. values for the concrete series. Water requirements increased with insoluble

residue for the constant slump concretes, but

decreased with the same variable for the 1:2.75

mortars. The MgO content of the cement

appeared significant in equations for both the

1 : 2.75 and the 1 : 4 mortars but not in the equations

for the concretes. As previously mentioned,

water used for normal consistency of the neat

pastes increased with total alkali. With the

1:2.75 and 1:4 mortars water requirement in- creased with increasing Na20 content, and with

the concretes it decreased with increasing K2O

content. As shown previously, the use of some of the

commonly determined variables in the computations produced significant relationships. In each

of the series of equations it was noted that the

additional use of certain minor constituents or

trace elements resulted in a slightly better fit or lower standard deviation values. Judging from

the tables showing the calculated contributions

of the various independent variables, the apparent

effect on the water requirements of some of these

trace elements or some variable associated with the

trace elements can be appreciable. It is recognized

that some of the minor constituents or trace elements which are closely related chemically

may supplement each other and should be considered together in the same manner as NaaO

and K2O in the total alkali. It is also possible

that, as with MgO, there is no appreciable effect until a certain minimum is present. However,

until more precise values are obtained, it does not

appear justified to employ the trace elements in other than linear relationships and until further

information is attained relative to their nature

and role in the chemistry of cement, they are being

treated separately rather than in any arbirtary

combination. There was some evidence that even

closely related oxides as Na20 and K2O or CaO

and SrO did not behave in the same manner in

their effects on the water requirements of the

cements.

The effect of the trace elements on water re- quirements was often different for the neat cement

pastes than for the two mortars, and, in general,

their effect on the concretes was not clearly demonstrated. The latter effect may possibly be ac- counted for by the fact that the cement constitutes

such a small percentage of the total volume of the

concrete, and effects of the small amounts of these

elements present in the cement are so diluted in a concrete mix by all of the other ingredients and

variables in the mix. The observation that effects 30

differ between pastes and mortars is harder to

explain. For example, in the equations for water

requirement of neat pastes (table 2-3), water

requirement consistently decreases with increasing

Cu content and increases with increasing Zr content. With both mortars, however, water requirement increases with increasing Cu content, and

with the 1 : 4 mortars it decreases with increasing

Zr content as well. (Equations with Zr as a variable with the 1 : 2.75 mortars are not shown

because they did not show a significant relationship for this element). This phenomenon may

be related to air content of the mortars, or to some effect associated with the sand, but there

appears to be nothing in these data on which a satisfactory explanation of this apparent contradiction can be based. Further studies of the role

of trace elements in cement reactions is indicated

as desirable.

The separation of the cements into two approximately equal groups based on the air content

obtained in the 1 : 4 mortar test enabled the computation of another series of equations to demonstrate the effect of air content on the water

requirements of the mortars and concretes. Comparisons of significant independent variables may be made between the pairs of eqs (1) and (2), (3) and (4), (5) and (6), or (7) and (8) in table 2-23 or between these equations and

those previously presented for AE+NAE and

for NAE cements in tables 2-8, 2-10, 2-15, and

2-20, respectively. The S.D. values for "low-air"

cements were in every instance less than those

obtained in corresponding equations for the NAE

cements presented in the previous tables. The

S.D. values for the "high-air" cements were lower

in 3 out of 4 of these equations than those obtained for the AE+NAE cements presented in the previous tables. It may also be noted that

the s.d. values for the coefficients of the independent variables in the present table are larger

than the s.d. values of the same variables in corresponding previous equations. This same

effect was previously noted in comparing the s.d. values for coefficients in the computations of the

"odds" and "evens" in an array of cements with

the s.d. values obtained when all cements were

used in an equation. The larger s.d. values obtained with the smaller number of cements in the

equations of table 2-23 may have caused a

coef./s.d. ratio of less than 1 for some of the

variables of marginal significance which resulted

in their elimination. It is also of interest to note

that in eq (1) of table 2-23 the air content (as

determined on the 1:4 mortars) was not a significant variable, whereas it was significant in the

1:4 mortars and concretes. Although the use of all possible combinations

of independent variables in trial equations would

have been impracticable, it is believed that with

the use of the high-low comparison (see ref. [6]) with the deviations most of the more important

variables on which tests were made have been

included in the equations presented.
6. Summary and Conclusions

(1) Tests were made on 199 portland cements

of different types and from different mills in order

to determine the interrelation of the cement

and concrete properties and the independent

variables associated with the various properties.

This section deals with the water requirements of neat pastes, of 1 :4 and 1 :2.75 motars of standard

consistency, and nominal Bji bags/yd^ concretes having a 5±1 in. slump, as well as with

the slump values of the 5}^ bags/yd^ concretes using a water-cement ratio of 0.635.

(2) The frequency distributions of the dif- ferent dependent and independent variables con- formed to the normal distribution, especially

for non-air-entraining cements, and are believed

to be fairly typical and to indicate the range of these variables which may be expected with

Portland cements.

(3) Comparisons of the estimated standard

deviations computed from all of the determined

values for the dependent variables with those of the respective computed multivariable equations

indicated that in each instance certain commonly

determined independent variables or cement

characteristics were associated with the water

requirements. The use in the equations of

certain minor or trace elements not commonly

determined resulted in equations with improved

ability to predict the water requirements of the

cements in many cases.

(4) Computations of multivariable equations by

the least squares method with all the cements used

in this investigation which included both the

air-entraining and non-air-entraining cements or only the non-air-entraining cements indicated that

a number of independent variables of these

cements were associated either directly or in- directly with the amounts of water required for normal consistency of the neat cements, for standard consistency of the mortars, or for concretes of constant slump; or were associated with

the slump values of concretes of constant watercement ratio. The following observations relate

to the results obtained with the combination of

both air-entraining and non-air-entraining portland cements and particularly to those equations

in which the AI2O3 content of the cement was

included as one of the independent variables:

(4.1) For neat portland cement pastes of

normal consistency, water requirement increased

with increasing air-permeability fineness, AI2O3,

CaO, SO3, or Zr; and decreased with increasing

Cu, P, or SrO. Of these variables, difference

in fineness appeared to have the greatest effect. (4.2) For the 1:4 cement to 20-30 Ottawa sand

mortars of standard consistency, water requirement increased with increasing AI2O3, silica modulus, MgO, or Na20 of the commonly determined variables, and with increasing Cu, Ti,

V, or Rb ; whereas it decreased with increasing air

content, fineness, insoluble residue, and Zr. Besides the air content, the AI2O3 and silica modulus values appeared to have the greatest

effect on the amount of water required for standard

consistency.

(4.3) For the 1:2.75 cement to gi-aded Ottawa

sand mortars of standard consistency, water

requirement increased with increasing AI2O3,

silica modulus, Na20, MgO, and SO3 of the com- monly determined variables, and with increasing

Cu, Li, and Pb; but decreased with increasing

air content of the 1 : 4 mortars (values for air content of the 1:2.75 mortars not being available),

insoluble residue, and SrO. In addition to the

air-entraining characteristics of the cements the

AI2O3 and silica modulus values appeared to have

the greatest effect on the water required for standard consistency.

(4.4) For the constant slump concretes, water

requirement increased with increasing insoluble

residue (one of the commonly determined variables of the cements), as well as with Co and Pb;

and decreased with increasing air content of the

concrete and Fe203, K2O, and Ba in the cement.

In addition to the entrained-air values the AI2O3

and Fe203 of the cement appeared to have the

greatest effect on the water requirements of the

constant slump concrete.

(4.5) For the constant-water-cement-ratio concretes, slump increased with increasing air content

of the concrete, and with Fe203 and K2O of the

commonly determined constituents of the cement,

as well as with Ba and Pb; and decreased with

increasing AI2O3, SO3, and Co in the cement. In

addition to the entrained-air values, the AI2O3 and

Fe203 contents of the cements had the greatest

effect on the slump of the concretes made with a constant water-cement ratio.

(5) The use of the A/F ratio or the potential

C3A instead of the percentage of AI2O3 in the

cements as one of the independent variables re- sulted in similar equations but with slight differ- ences in the coefficients of the other independent

variables.

(6) When equations were computed using only

the non-air-entraining cements the same independent variables were generally significant but

not to the same degree as when the air-entraining

cements were included in the computations.

(7) Equations computed for the "odds" and

"evens" in an array of cements were in general

concordant and enhanced confidence in the

coefficients of the different independent variables

obtained from the complete set. The coefficients of the independent variables and the standard

deviation of the equation computed from all the

cements were bracketed by those computed from

the "odds" and "evens" in the array. The

standard deviation attributed to each of the coefficients of the independent variables was almost

always greater for the "odds" and "evens" when

compared to the values for the entire lot.

31
(8) The equations computed for the mortars

and concretes using the cements having less than

7.0 percent air contents in the 1:4 mortar test and

those having 7.0 percent or more air in this test demonstrated that the effect on water requirements and slump of many of the independent

variables was different for the low-air and highair cements. However, with the smaller number

of samples in each of the groups, the uncertainty

with respect to the individual coefficients of the

different independent variables was usually

greater. With a few exceptions the variables

indicated in the computations for the AE+NAE

or the NAE cements as being highly significant were also significant in computations for the

the "low-air" and "high-air" groups of cements.

The variables of marginal significance in equations

for the AE+NAE and NAE cements were often

not significant when the computations were made

for the "low-air" and "high-air" cements.

(9) In general, slump and water requirements

of the concretes were significantly related to water requirements of the 1 :4 and 1 : 2.75 mortars

with the relationship being better with the

AE-j-NAE cements than with NAE cements

alone.

(10) The lack of precision of the equations is attributed in part to various factors such as the

leeway in water used for normal and standard

consistency determinations, normal variability of

test results, lack of adequate range of values for some of the independent properties known to be

carefully controlled in manufacture, and lack of information of certain independent variables as well as the effect of interaction of so-called in- dependent variables.

Acknowledgments are made to the heads of branch laboratories of the National Bureau of Standards at AUentown, Pa., Denver, Colo., San

Francisco, Calif., and Seattle, Wash., G. Stiller,

O. H. Cox, O. C. Marek, and Frank Winblade,

respectively, as well as their associates and co- workers, and to M. R. DeFore and Leonard Bean

and associates in the Washington laboratory for making the many tests involved. Acknowledgments are also made to D. N. Evans for collecting,

checking, and compiling the data.

7. References

[1] Federal Test Method Standard: Cements, Hydraulic, [6] Interrelation between cement and concrete properties:

Sampling, Inspection, and Testing, SS-C-158. materials and techniques, of this paper Section 1. [2] Standard Method of Test for Normal Consistency of [7] D. A. Abrams, Discussion on portland cement contain- Hydraulic Cement, ASTM Designation C 187-58. ing vinsol resin, Proc. ASTM 45, 755 (1945).

[3] Standard Method of Test for Compressive Strength of [8] R. F. Blanks and H. L. Kennedy, The Technology of Hydraulic Cement Mortars (using 2-in. cube speci- Cement and Concrete, Vol. 1, Concrete Materials,

mens), ASTM Designation C 109-58. pp. 247-250, (John Wiley & Sons, Inc., New York,

[4] Standard Method of Test for Air Content of Hydraulic N.Y.).

Cement Mortar, ASTM Designation C 185-59.

[5] R. L. Blaine, J. C. Yates, and J. R. Dwyer, The testing

of Portland cement containing interground vinsol

resin, Proc. ASTM 45, 732 (1945).

32
Section 3. Occurrence of Minor and Trace Elements in

Portland Cement

R. L. Blaine, Leonard Bean, and Elizabeth K. Hubbard

Minor and trace elements in 186 portland cements were determined by spectrographic

analyses. The semiquantitative values obtained ranged up to 1 percent for Ti and Mn, to

0.5 percent for P, and Zr, to 0.2 percent for Ba and Zn, to 0.1 percent for V, to 0.05 percent

for Cu, Mo, and Pb. Other elements such as Cr, Li, Ni, Co, Rb, Ag, B, and Sn were found

in lesser amounts in some of the cements. The quantities of NajO, KjO, and SrO as deter- mined by flame photometric methods were determined in 199 portland cements. The

frequency distributions are presented and the effect of these minor and trace elements on

the oxide values and the calculated compound composition values are discussed.

Contents

Page

1. Introduction 33

2. Materials 33

3. Testing procedures 34

4. Results of tests 34

5. Discussion 34

6. Summary 36

7. References 36

1. Introduction

It has long been recognized that portland

cements contain small quantities of elements other

than those present in the larger quantities to which hydraulic and other properties are generally

attributed. These trace elements have been

referred to as minor elements, minor constituents

and even as impurities. The presence of these

elements in portland cement may result from their

existence in the raw materials from which the

cement is made, from the ash in the coal used in

the burning of the clinker, from the lining of the

cement kiln, from the attrition of grinding media

and lining of the grinding mill, or may in some

instances be added to enhance the clinkering

characteristics or the properties of the cement or even to procure a desirable by-product.

The importance of the minor and trace elements

in stabilizing the silicate compounds such as are formed in the manufacture of cement was shown

by Bates and Klein in 1917 [1].^ In papers pre- sented at the 1952 Third International Symposium

on the Chemistry of Cement, Jeffery [2] and

Nurse [3] summarized and discussed work in this

field. Further summaries of the effects of minor

and trace elements were made in the 1960 Fourth

International Symposium on the Chemistry of

Cement by Nurse [4], Welch and Gutt [5], Heilmann [6], Locher [7], Woermann [8], Toropov [9], and others. It was concluded by a number of

these authors that the presence of minor components can greatly influence the properties of

the major compounds and therefore also the

properties of the portland cements, and that

further information relative to the minor and

trace elements was needed.

There have been numerous reports of the

presence and effect of some of the minor and trace elements such as Na, K, Sr, Ti, P, and Mn, but

very little information is available relative to other

elements. It appeared desirable, therefore, in the

Study of the Interrelations Between Cement and

Concrete Properties to obtain further information on the occurrence of all minor and trace elements

in Portland cement and to determine, at least in a semiquantitative manner, the amounts of these

elements which may be present.

The effects, if any, of these minor and trace elements on the physical properties of the cements

will be discussed in other sections in this series dealing with specific properties of the cements and

concretes.

2. Materials

The 186 Portland cements analyzed in this investigation have been described in a previous

section [10]. The samples are believed to be

' Figures in brackets indicate the literature references at the end of this

section.

fairly representative of different types of portland

cement produced in different areas of the United

States. Only a few of the cements were procured

from overseas.

33
3. Testing Procedures

The procedures and apparatus used for the

semiquantitative spectrographic analyses were as

follows: A 5 mg portion of the portland cement

sample was mixed with 2 mg of high-purity graphite powder which acted as a buffer to assist in volatilizing the sample. This charge was placed

in a graphite electrode having a shallow cup, and

was vaporized and excited in a d-c arc with a current of 15 A. The light from the arc, passing

through a slit of the spectrograph was dispersed

into a spectrum and this was photographed in the

spectral range 2200-4800 A on Eastman 33 plates,

4600-6000 A on Eastman II-F plates and 6600-

8000 A on Eastman I-N plates. The spectrograph

used for this work had a Wadsworth mounting of a concave grating, the grating having 15,000 lines

per inch and a radius of curvature of 21 ft. The

spectrograph produced a spectrum with linear

dispersion of 5 A per mm in the first order.

The spectrograms of the cement samples were compared with those of synthetic standards of

3CaOSi02 containing known amounts of the

trace elements commonly found in portland

cements, and semiquantitative values were as- signed each element present based on a combination of visual estimations and photometric measurements. Duplicate determinations were made

on all samples.

The determinations of Na20 and K2O were made by Federal Specification methods [11] and

SrO by a flame photometric procedure which has

previously been described [12].

4. Results of Tests

The frequency distribution of the minor and

trace elements as determined by the spectrographic analyses is presented in table 3-1, and

the frequency distribution of the minor and trace

elefnents as determined by flame photometric

techniques is presented in table 3-2. Elements

other than those indicated in the tables were

not detected or were present in quantities less than 0.001 percent. The semiquantitative values

reported in table 3-1 are for the elements. If they had been reported as oxides, as is customary

in cement analyses, the values would be cor- respondingly higher.

A comparison of values for Mn obtained by the

spectrographic analyses with those obtained by

regular chemical analyses on a number of cements

indicated close agreement between the results obtained by the two methods.

The frequency distribution of the cements with

the greatest quantities of the minor and trace elements as found in different areas of the United

States is presented in table 3-3. It may be noted

that a number of cements obtained from east

of the Mississippi River, areas 1 through 5, had

high values for Mn, P, and Zn. Although not

indicated in table 3-3 the highest values for Zr, 0.5 percent, was from area 5. A number of the

cements obtained from areas 6 and 7, between the

Mississippi River and the West Coast area, had

high values for Co, Cr, Mn, Ni, Pb, Ti, and Zr,

whereas a number of cements obtained from the

West Coast areas had high values for Co, Cu,

Li, Mo, V, and Zn. The prevalence as well as variety of the larger quantities of rnjast of the

minor and trace elements was greater' west of the

Mississippi than in the eastern part of the country.

5. Discussion

In many instances a number of different types

of cements were obtained from a single manufacturing plant. The distribution of values pre- sented may therefore not truly represent that

distribution of values which would have been

obtained if ah equal number of cements had

been obtained from each of the mills. The reported oxides and calculated compound

composition values resulting from the regular

chemical analyses of portland cement may be

in error as a result of the presence of the minor

and trace elements. The effect of the presence

of these elements on an ordinary analysis, if not

removed or determined, is described in a number

of standard texts [13]. For example, Ba would

normally be expected to be included with the

AI2O3 value. Some of the Co would also be

included with the AI2O3 but most of the Co would

be in the Ca value. The Cr would also be included

with the AI0O3 as would a portion of the Cu; the

remainder of the Cu would probably be lost. L

is generally lost in the course of an ordinary

analysis together with the other alkalies when

not determined. Some of the Mn may be in- cluded with the AI2O3, some with the CaO, precipitated as calcium manganite or manganese

oxalate, and some will be included with the

MgO. When referee methods are used, the Mn

is removed. Mo, if present, would probably be

included with the AI2O3, whereas some of the Ni

would be included with the CaO and some would

be lost. The P would be included with the

AI0O3. Pb may also be distributed between the

AI2O3, the CaO, and the MgO. The Rb is probably lost by our present methods but may possibly

affect the K2O values. In the regular and referee

chemical methods the SrO is included with the

CaO. The Ti, unless determined, is included

wfth the AI2O3 as is part of the V, the remainder

being reported with the CaO. Some of the Zn

34
Table 3-1. Frequency of occurrence of different percentages of minor and trace elements in portland cements as determined

by spectrographic analysis

Element Lower limit of reporting

Cements below

lower limit of reporting

Approximate percentage present as elements

0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0

79

1 55

39

15

4

58 26 6 4 26

6

18

10

2752

1086

55

1

1112

2

26

5

78

4

56 11 8 1 658

1 43

546 22 i 4 1 9

1165

1 533

5

1 3 2

7128

6

49

4

11

1

115 14 1 62

1 83

25

2

9

2

1 83 1 1

Ba.

Co.

Cr. Cu.

Li.. Mn

Mo.

Ni., P.. Pb. RbTi..

V.-.

Zn.. Zr..

Percent

0.01

.001

.001

.001 .005

.01

.001

.001

. 1 .001 .001 .05

.01

.01

.001

13 139

15 168

1 170

16 172

155

1450

83

162

1

Ag, B, and Sn were also present in some cements in quantities less than 0.001 percent.

Table 3-2. Frequency distribution of oxides of minor and trace elements in portland cements as determined by flame

photometer method

Percentage present

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 Oxide to to to to to to to to to to to to to to to

.05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75

NazO 16 34 48 22 27 10 12 12 4 3 6 2 1 0 1 SrO.. 22 70 41 24 11 12 9

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.1 1.2 1.3 Oxide --- - --- to to to to to to to to to to to to to to

0.1 .20 .30 .40 .50 .60 .70 .80 .90 1.00 1.10 1.2 1.3 1.4

K2O 8 21 24 23 38 27 22 15 15 4 2 Total Alk as Na20 (Na20

+0.658 K20)..._ 2 12 25 25 39 36 24 19 12 4 1

' 2

Table 3-3. Frequency distribution of cements with the larger quantities of minor and trace elements in different areas of the United States

Minor or trace element Quantity present percentage Area in TJSA*

1 2 3 4 5 6 7 8 9 10 11

Ba 0. 1-0.

2

0. 005-0. 01

0. 02

0. 02-0. 05

0. 01-0. 02

0. 2-0. 5

0. 005-0. 05

0. 01-0. 02

0. 1-0. 5

0. 01-0. 05

0. 5-1. 0

0. 05-0. 10

0. 1-0. 2

0. 02-0. 50

2

11

1 1 4 2 Co 1 1 12

3 Cr 1 3

1

1

112

13

2

3

5

13

112

53

12

Cu _.

._ 2 1 LiMn 6 1 4 3 Mo 2 Ni 2 3

2

1 1 13 4 4

2

13

2

P 6 Pb 5 Ti" 1 1 4 2

3

1 v.. 2 3

2

5 Zn 1

1 5 Zr 1 3 4 5 3

•Area No. States included—

1 -- Eastern Pennsylvania, Maryland.

2 New York, Maine.

3 Ohio, Western Pemisylvania, West Virginia, Michigan.

4 Illinois, Indiana, Kentucky, Wisconsin, Alabama, Tennessee.

5 Virginia, Georgia, Florida, Louisiana, South Carolina, Mississippi. 6 Iowa, Eastern Missouri, Minnesota, South Dakota, Kansas. "One from country other than U.S.A.

Area No. States included

7 __ Western Missouri, Nebraska, Oklahoma, Arkansas, Texas.

8 Colorado, Arizona, Montana, Utah, Idaho.

9 -- Northern California.

10 Southern California.

11 Washington, Oregon.

35
would be included with the AI2O3 and the re- mainder precipitated as the oxyquinolate causing an error in the MgO value. The Zr would also

be included with the AI2O3. Although the quantities of the minor and trace elements are small

it may be noted from the above discussion that

Ba, Cr, Mo, P, Ti, Zr, as well as portions of the

Co, Cu, Mn, Pb, V, and Zn are included with the

AI2O3. The computed tricalcium aluminate value

would then be larger than actual whereas the

tricalcium sUicate value would be smaller than

actual. This is in agreement with the report by

Insley and coworkers [14] and the summary

presented by Lea and Desch [15], p 143. A more serious effect of the minor and trace elements has also been discussed by Lea and Desch

(15), p. 139, where it was shown that minor components can cause displacements of the clinker

equilibrium fields. As mentioned in the introduction, the effect, if any, of these minor and trace elements on the

properties of cement will be treated in other

sections on the properties of the cements in this

investigation.

6. Summary

Minor and trace elements in 186 portland

cements were determined by spectrographic analyses. The semiquantitative values obtained

ranged up to 1.0 percent for Ti and Mn, to 0.5 percent for P and Zr, to 0.2 percent for Ba and Zn,

to 0.1 percent for V, to 0.05 percent for Cu, Mo,

and Pb, to 0.02 percent for Cr, Li, and Ni, and to

0.01 percent for Co and Rb. Ag, B, and Sn were

present in some portland cements in quantities

less than 0.001 percent. The quantities of Na20,

K2O, and SrO as determined by flame photometric

methods in 199 portland cements were also determined.

The frequency distribution of the minor and

trace elements in portland cements are presented

as are the frequency of occurrence of high values

in different areas of the United States. The effect of these minor and trace elements on

the oxide values obtained by routine analyses

and the calculated compound composition values

are discussed. In view of the fact that many of

the trace elements would be included with the

alumina, the calculated tricalcium aluminate

value is probably high and the tricalcium silicate value is correspondingly low. Attention is also called to the effect of minor elements on the

equilibrium values of the major components.

The effect, if any, of the minor and trace ele- ments on the physical properties of the cements

will be presented in future sections dealing with

properties of these cements.

7. References

[1] p. H. Bates and A. A. Klein, Bureau of Standards

Tech. Paper 78 (1921).

[2] J. W. Jeffery, The Tricalcium Silicate Phase, Proc. Third International Symposium on the Chemistry

of Cement, London (1952), p. 30.

[3] R. W. Nurse, The Dicalcium Silicate Phase, Proc. Third International Symposium on the Chemistry

of Cement, London (1952), p. 56.

[4] R. W. Nurse, Phase Equilibria and Constitution of Portland Cement Clinker, Proc. Fourth Inter- national Symposium on the Chemistry of Cement,

Washington (1960), p. 9.

[5] J. H. Welch and W. Gutt, The Effect of Minor Components on the Hydraulicity of the Calcium Sili- cates, Proc. Fourth International Symposium on

the Chemistry of Cement, Washington (1960),

p. 59.

[6] T. Heilmann, Reactions of Coal Ash with Portland Cement Clinker During the Burning Process, Proc. Fourth International Symposium on the Chemistry

of Cement, Washington (1960), p. 87.

[7] F. W. Locher, Solid Solution of Alumina and Magnesia

in Tricalcium Silicate, Proc. Fourth International Symposium on the Chemistry of Cement, Washington (1960), p. 99.

[8] E. Woermann, Decomposition of Alite in Technical

Portland Cement Clinker, Proc. Fourth Inter- national Symposium on the Chemistry of Cement,

Washington (1960), p. 119.

[9] N. A. Toropov, Solid Solutions of the Minerals of Portland Cement Clinkers, Proc. Fourth Inter- national Symposium on the Chemistry of Cement,

Washington (1960), p. 113.

[10] Interrelations between cement and concrete properties; materials and techniques, of this publication.

[11] Federal Specifications SS-C-158c Amendment 1; Cements, Hydraulic, Methods for Sampling, Inspection and Testing, May 25, 1954.

[12] J. J. Diamond, Photometric determination of stron- tium in portland cement. Anal. Chem. 27, 913, June 1955.

[13] W. F. Hillebrand, G. E. F. Lundell, H. A. Bright,

and J. J. Hoffman, Applied Inorganic Analysis, 2d

Edition (John Wiley & Sons, Inc., New York,

N.Y.).

[14] H. Insley, E. P. Flint, E. S. Newman, and J. A.Swenson, J. Res. NBS, 21, 355 (1938) RP1135.

[15] F. M. Lea and C. H. Desch, The Chemistry of Ce- ment and Concrete (revised edition) (1956), Edward Arnold (Publishers) Ltd.

36

U.S. GOVERNMENT PRINTING OFFICE: 1965 O—748-580
Announcement of New Publications in

Building Science Series

Superintendent of Documents,

Government Printing Office,

Washington, D.C., 20402

Dear Sir: Please add my name to the announcement list of new publications to be

issued in the series: National Bureau of Standards Building Science Series.

Name , Company

Address

City State Zip Code

(Notification key N-339)



THE NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards is a principal focal point in the Federal Government

for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. Its responsibilities include development and

maintenance of the national standards of measurement, and the provisions of means for making measurements consistent with those standards; determination of physical constants and

properties of materials; development of methods for testing materials, mechanisms, and

structures, and making such tests as may be necessary, particularly for government agencies;

cooperation in the establishment of standard practices for incorporation in codes and specifications; advisory service to government agencies on scientific and technical problems; invention

and development of devices to serve special needs of the Government; assistance to industry,

business, and consumers in the development and acceptance of commercial standards and

simplified trade practice recommendations; administration of programs in cooperation with

United States business grojups and standards organizations for the development of international standards of practice; and maintenance of a clearinghouse for the collection and

dissemination of scientific, technical, and engineering information. The scope of the Bureau's activities is suggested in the following listing of its four Institutes and their organizational units.

Institute for Basic Standards. AppHed Mathematics. Electricity. Metrology. Mechanics.

Heat. Atomic Physics. Physical Chemistry." Laboratory Astrophysics.* Kadiation Physics. Radio Standards Laboratory:* Radio Standards Physics; Radio Standards Engineering. Office of Standard Reference Data.

Institute for Materials Research. Analytical Chemistry. Polymers. Metallurgy. Inor- ganic Materials. Reactor Radiations. Cryogenics.* Materials Evaluation Laboratory.

Office of Standard Reference Materials.

Institute for Applied Technology. Building Research. Information Technology. Performance Test Development. Electronic Instrumentation. Textile and Apparel Technology

Center. Technical Analysis. Office of Weights and Measures. Office of Engineering Standards. Office of Invention and Innovation. Office of Technical Resources. Clearinghouse

for Federal Scientific and Technical Information.**

Central Radio Propagation Laboratory.* Ionospheric Telecommunications. Tropospheric

Telecommunications. Space Environment Forecasting. Aeronomy.

* Located at Boulder, Colo., 80301.

** Located at 5285 Port Royal Road, Springfield, Va., 22171.
U.S. DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20230

POSTAGE AND FEES PAID

U.S. DEPARTMENT OF COMMERCE

OFFICIAL BUSINESS