Uhi 'v't::.K0! 1 '( Ui- iLLINOiS Ui~8ANA, ILLINOIS

CIVIL ENGINEERING STUDIES l A STRUCTURAL RESEARCH SERIES NO. 313

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AN INVESTIGATION INTO THE RELATION BETWEEN THE STRENGTH AND DENSITY

OF NORMAL CONCRETE

A Thesis by

ENRIQUE I. ESPINO

UNIVERSITY OF ILLINOIS URBANA, ILLINOIS SEPTEMBER 1966

AN !NVESTIG.t\T!ON INTO THE RELATiON BETWEEN

THE STRENGTH AND DENSITY OF NORMAL CONCRETE

A Thes!s by

Enrrque ~o Esp!no

Augusts 1966 University of III inois

Urbana, 1'/l! nor s

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ACKNOWLEDGEMENTS

This study is presented as a master's thesis, written under

the direction of Dr. K. Preiss, Assistant Professor of Civil Engineering

and of Nuclear Engineering at the University ofl 11 inoi~! The author

wishes to express his gratitude to Dr .. Preiss for his valuable and

pertinent guidance during the course of this investigation.

The writer wishes also to acknowledge the help and advice of

Dr. M. A. Sozen, Professor of Civil Engineering, and of Dr. H. K. Hi·1sdorf,

Associate Professor of Civil Engineering, both at the University of

111 i no is.

The experimental work was done at the Structural Research

Laboratories of the Department of Civil Engineering, at the University

of 111 inois. The gamma ray apparatus used was designed and cal ibrated

by Dr. Preiss.

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TABLE OF CONTENTS

1. I NTRODUCT ION

REVIEW OF REPORTED WORK.

3. SPECtMENS AND TEST PROCEDURE

3.1. General ...

3.2. Materials and Test Procedure.

3.2.1. Aggregates

3·2.2. Cement .

3.2.3. Mixing

3.2.4. Compaction

3.2.5. Curing ..

3.2.6. Measurements and testing.

4. RESULTS ...

4.1. Results for Each Mix

4.2. Results for Each Group

4.3. Results for All Mixes ..

5. CONCLUSIONS.

TABLES .

FIGURES.

LIST OF REFERENCES

APPEND I X . . . . .

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LIST OF TABLES

Table Page

DETAILS OF MORTAR MIXES (GROUP 1). 23

2. DETAILS OF CONCRETE MIXES WITH 3/8 INCH MAXIMUM SIZE AGGREGATE (GROUP 2) . .. • ..... . 24

DETAILS OF CONCRETE MIXES WITH 3/4 INCH MAXIMUM SIZE AGGREGATE (GROUP 3) . . . ..... . 25

4. COEFFICIENTS OF VARIATION OF CYLINDER STRENGTH. 26

5. SLOPES OF THE STRENGTH-DENSITY CURVES AT SELECTED DENSITIES .... 0 ••••• 0 • • • • • • • • • • 27

Al. DENSITIES AND PARAMETERS Z/A FOR THE CALIBRATION S P E C I MEN S • . . . . . . . . 0 • • • • • • • • • • 5 1

A2. ANALYSES AND CHEMICAL COMPOSITION FACTORS C FOR THE COMPONENTS OF THE CONCRETE .. 0 ••• 0 • • 51

A3. COMPARISON OF DENSITIES BY GAMMA RAY AND WEIGHING METHODS 0 0 • • • 0 • • • • 0 • • • • • • • • 52

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L!ST OF F~GURES

Figure Page

1. STRENGTH vs DENSITY FOR NO-FINES CONCRETE 28

2. STRENGTH vs RELATiVE AIR VOIDS FOR SERIES 2G. 29

3. DENSITY vs RELAT!VE AIR VOIDS FOR SERIES 2G 29

4. STRENGTH vs RELATIVE AIR VOIDS AT VARIOUS CEMENT CONTENTS . . 30

5. STRENGTH vs RELAT!VE VOLUME OF CEMENT AT VARIOUS AIR VOIDS CONTENTS. .. 30

6. RELATION BETWEEN STRENGTH RATIO AND DENSITY RATIO.. 31

7. STRENGTH vs PERCENT AIR AT VARiOUS CEMENT CONTENTS. 31

8. STRENGTH vs DENSITY FOR MIX A .

STRENGTH vs DENSITY FOR MIX B .

10. STRENGTH vs DENSITY FOR MiX C

11. STRENGTH vs DENSITY FOR MIX D .

12. STRENGTH vs DENSITY FOR MIX E

13. STRENGTH vs DENSiTY FOR MiX F

14 .. STRENGTH vs DENS I TY FOR MORTARS 0

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150 STRENGTH vs DENS I TY FOR CONCRETES W1TH 3/8 I NCH GRAVEL 0 39

16. STRENGTH vs DENSITY FOR CONCRETESW!TH 3/4 INCH GRAVEL. 40

17·

Al.

A2.

A3·

STRENGTH vs DENSITY FOR ALL MIXES 0 o.

DIAGRAM OF THE APPARATUS SHOWING A SPECIMEN iN POSITION FOR DETERMIN"ING THE DENSITY ..

BLOCK D"IAGRAM OF THE DETECT ION SYSTEM .

DISTRIBUTION OF PULSE HEIGHTS OBSERVED.

A4. ~ vs p x Z/Ao

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LIST OF FIGURES (Continued)

Figure

AS. CHEMICAL COMPOSITiON FACTOR C vs WATER CONTENT ..

. A6. LOG R vs THICKNESS x FOR ALUMINUM AND LUCITE .

A7. COUNT RATE R vs D!STANCE e FOR LUC!TE . 0

A8. COUNT RATE R vs DISTANCE e FOR ALUMINUM.

A9. COMPARISON OF DENSITIES OBTAINED BY GAMMA RAY APPARATUS WITH DENS!TIES OBTAINED BY WEIGHING AND

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MEA SUR I N G . . 0 • 0 • 0 0 • • • 0 • 0 0 • • • • 0 6 1

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1 • I NTRODUCT ~ ON

The cyl inder crushing test is the most common method for

cantrall ing the qual ity of the concrete used in a structure. In this

test, cyl inders of the same concrete as In the structure are cast,

and then crushed in a standard way; the crushing strength is used as

a measure of qual ity. Although this method of qual ity control has

been used for many years~ It suffers from the weakness that the concrete

in the structure itself !s not tested; it is assumed that the cyl inders

are representative of the concrete in the structure. A further dis-

advantage of the concrete crushing test is that it usually takes 7 to

28 days to obtain the test results. By that time the concrete in the

structure has hardened and removal of substandard portions of the

structure is difficult and expensive.

It may eventually be possible to determine with rel iabil ity

the strength of the concrete in a structure by a series of non-destructive

tests. It is not at all clear how this promising goal may be attained;

the improvements In concrete engineering which would follow would be

revolutionary. Among the non-destructive test methods made available

by modern developments in technology is that of density measurement by

gamma ray t ran s m iss ion (1) '\ (2). s u c hap par a t u sis des c rib e din the

appendix to this thesis.

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ftNumbers in parentheses refer to entries in the 1 ist of references.

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Th~ qual ity of the concrete in a structure is determined by

the properties and proportions of the aggregate~ cement, water and

addi tives used, by the mixing and compaction procedure, by the curing of

the concrete after placing and by the age at which the concrete is

tested. In particular, the strength of concrete is greatly influenced

by the water-cement ratio and the relative volume of air in the mix.

Since aggregates, cement, water and air have different specific, weights,

the overall density of a concrete mix will depend upon the relative

amounts of these materials present. A relation between the strength and

the density of a particular concrete mix may therefore be expected.

This r~lation, if it could be establ ished, would be unique only for mixes

with identical cement and aggregates, proportions, curing, age at test­

ing and strength testing procedure.

The density of concrete in a structure can be measured non­

destructively using gamma radiation; if the relation between strength

and density for a particular cor.crete under the relevant curing condi­

tions were known, the strength could be inferred from the value of density

obtained.

In order to decide whether or not the measurement of density

could be used to give a reasonably accurate value of the strength of

normal concrete it is necessary to know the sensitivity of the strength

of concrete to changes in the density. This experimental investigation

led to the conclusion that an error of 1 percent in density measurement

of a given concrete would result in an error of approximately 8 percent

in the inferred strength. Accuracy of 1 percent in density measurement

can easily be attained by the gamma ray transmission method(see Appendix).

3

Density measurement can therefore give a useful determination of the

strength of a particular concrete.

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2. REVIEW OF REPORTED WORK

The purpose of this rnvestigation is to find whether the

relation between strength and density of concrete is such that density

measurements can be used for strength determination. To this end a

more complete understanding of the factors affecting the strength and

the density of concrete is helpful; a discussion of some past work on

this subject is presented in this chapter.

Feisenheiser and Wasil (3), following an experimental research

program on steel-aggregate concrete, postulated that the strength of

any concrete of given ingredients is proportional to its density. No

data on the strength-density relation for normal concrete is however

given.

Hanson (4) conducted some experiments where the expanded fines

of 1 ightweight concrete were replaced by an equal 'volume of river sand.

The total amount of cement was varied to give a strength range of 3 to

6 kips per square inch. It was found (4) that, in general, the structural

properties were improved, but this improvement was achieved only with a

considerable increase in unit weight. ~

Neville (5:456)" discussed the properties of no-fines concrete

and wrote that the strength of n6-fines concrete varies generally between

200 and 2000 pounds per square inch, depending mainly on its density.

Figure 1, from a paper by Mcintosh, Balton and Muir (6:692) on the use

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HThe number in parentheses after the colon indicates the page number in the reference cited.

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of no-fines c2ncrete as a structural material, shows an increase in

the compressive strength of no-fines concrete as its density increases.

These three reports, discussed above, show a very general and

simpl ified rule that the strength increases with density. This is in-

teresting, but of 1 ittle use for this investigation. A more specific

relation between strength and density is needed, from which one could

determine the strength of concrete to a useful order of accuracy.

Itis generally known that the strength of concrete made

from given materials depends upon the properties of these materials.

The water-cement ratio and the amount of air in the hardened concrete

have in particular great influence on the strength (5:216). Some

investigations (7), (8), (9), (10), (11), and (12) on the effects of

air, cement and water content on the strength of concrete are reviewed

below.

Feret (7), (8), following an experimental program, suggested

equation (1) to estimate the strength of a mortar.

p 2.0

( c ) K 1 s ( 1 )

Here P is the compressive strength, c is the ratio of the

volume of ce~ent added to the volume of the fresh mix and s is the

ratio of the volume of sand to the volume of fresh mix. K is a pro-

portional ity constant establ ished experimentally, which depends on the

qual ity of the cement used, the age at which the material is tested, the

test specimen and the testing method. Feret explained that in equation

(1) the value of "two for the exponent is only an approximation; this

exponent is always larger than one and in most cases close to two (7).

6

Fere~ modified equation (1) to take into account the effect

of a material present in the mix other than cement, sand and water. This

other material, which may be eIther coarse aggregate or fine sand, is

assumed to be inert relative to the cement used. The modified equation

is of the form

P c (2) - m -

where the parameters P, K, c and s are as defined before and m is

defined as the ratio of the volume of the coarse aggregate or the fine

sand, to the total volume of the fresh mix.

Neville (5:216), discussing Feret1s work, wrote equation (1) as:

p (3)

where: P is the compressive strength of the concrete

c is the absolute volume of cement used in the mix

e is the absolute volume of water used in the mix

a is the absolute volume of air in the resulting concrete

K is a proportional ity' constant depending on the cement used, shape

and size of the test specimen, and test procedure.

Since the amount of water in the mix will determine the porosity

of the cement paste at any state of hydration the effect on the strength

I of both the voids due to compacting procedures and the voids due to

I water-cement ratio should be considered (5:216)~ Results presented by

Powers (9) show that the strength does indeed depend upon the ratio of

I the volume of m1xingwater plus air vOids to the weight of cement in the

concrete.

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Talbot and Richart (10: 10) wrote in 1923, "Most authorit.ies

on concrete are in accord with the principle that, other things being

similar, ~ithin certain i imits the strength of concrete increases with

the quantity of cement used and with the density or sol idit.y of the

resulting concrete" .. 0" Some of their results (10:30) relating the

compressive strength of hardened concrete and the volume of voids in

a unit volume of fresh concrete, are presented here in Figure 2. These

are the results from a series of tests (Series 2G) where the size of

aggregates and the gradation of the aggregates were varied. All

specimens in this series were made with one part of cement to five

parts of mixed aggregates by volume. This series of tests covered a

range of relative volume of air voids, from 0.10 (very dense concrete)

to 0.40 (very porous concrete), a large range of particle size and a

large variety of aggregate gradations. The relative volume of air

voids was defined (10) as the volume of voids in a unit volume of

f res h con c ret e . Tal bot and Ric ha r t (1 0 : 33 ) con c 1 u d edt ha t ". 0 0 w hen the

great range of size of particles and the variety of gradation are

considered, the close relatton between the magnitude of the vords and the

compressive strength of concrete is striking."

Figure 3 shows a curve presented by Talbot and Richart (10:37)

where the dens'ity of concrete is seen to vary 1 inearly with the volume

of voids in the mixture. From the results presented in Figures 2 and 3

Talbot and Richart concluded (10~37) "oo.for the same cement and the

same kind of aggregate the strength of the concrete is a fair~y close

function of its weighto ll

8

Another group of tests on the strength of concrete cyl inders

(Series 211) was reported by ~lbot and Richart (10:64) where an

equation representing the test results was proposed in the following

form:

2·5 S = 32000 ( c ) (4)

'v + c

Where S is the compressive strength of concrete cylinders at 28

days in pounds per square Inch

c is the absolute volume of cement per unit volume of fresh

concrete

v is the volume of voids in a unit volume of concrete.

This equation is in a similar form to the equation presented

by Feret (7), (8), where the strength of mortars and concretes is pre-

dieted by equations (1) and (2)0

All mixes in Series 211 of reference (10) were made with an

amount of water equal to their corresponding basic water content. The

basic water content was defined (10) to be that amount of water which

will give the greatest density and least volume of voids. Talbot and

Richart (10) considered the effect on the strength of concrete, at the

basic water content, of the volume of cement and the volume of voids.

FIgure 4 (10:78) shows the effect of a variation of the volume of voids

on the strength, at a constant volume of cement. Three curves are shown

indicating three different volumes of cement. Figure 5 (10:78) shows

the effect on strength of a variation in the volume of cement used, at

a constant volume of volds. These two sets of curves show:

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a) for a given mix, with a fixed volume of cement, the

strength decreases as the r~lative volume of voids in

the hardened concrete increases

b) at a given volume of voids in the mix the strength of

the concrete will increase with an increase in the rela-

tive volume of cement used.

Glanville, C01lins and Matthews (11) crushed a number of

specimens of partially compacted concrete. Their results (11:7) are

plotted in Figure 6 and show that the strength ratio increases with an

increase in density ratio, where the strength and density ratios are

the ratios of the strength and density of the partially compacted concrete

to the strength or density of the same concrete if compacted In standard

manner. The slope of the curve in Figure 6 is such that if the density

ratio decreased by 1 percent, at a value of 1.0, the strength "ratio

would decrease by approximately 8 percent. This agrees with the results

reported here in Chapter 4.

The degree of compaction of a mix will affect the total volume

of voids, and since an increase in the total volume of voids will cause

a decrease in density, it can be concluded that a well-compacted mix will

have a large density and high strength compared to a partially-compacted

mix.

The effects of air voids are considered also by Walker and

Bloem (12) in a discussion of the qual ity control of air-entrained

concrete. A set of curves (12:7) reproduced in Figure 7, indicate that

the strength reduction due to an increase in the amount of entrained air

is more pronounced in rich mixes (large amounts of cement) than in lean

mixes.

10

It may be concluded from the work reviewed here, that for

a particular set of ingredients, mix proportions, curing conditions

and met~od of testing, the compressive strength of normal concrete

decreases as the volume of air In the mix increases. This increase

in entrained air can be detected, non-destructively, by a density

measurement.

Many investigators (13), (14), (15), (16), (17), (18), have

reported on the relation between the strength of concrete and the

aggregate size. There is an overwhelming amount of evidence that

strength does not depend only on the water-cement ratio, but also depends

on the properties of the aggregates used.

Several investigators have reported the effect of aggregate

grading on the strength and densIty of normal concrete. Glanville,

Co11 ins and Matthews (11) found that the effect on the strength of

quite large changes in grading was Insignificant. Singh (19) found that

both the strength of concrete and the density decreased as the specific

surface of the aggregates increased, for constant water-cement and aggre­

gate-cement ratios. He found further that the strength of a concrete of

given proportions will not be affected by the grading of the aggregates,

provided the specific surface remains constant.

Popovics (20) investigated various factors which may affect

the density of concrete. The three most significant factors were found

to be:

a) Average specific gravity of the aggregates

b) Air content of the concrete mix

c) For concretes of constant consIstencies, the grading of

the aggregates.

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It~an be concluded that the properties of the aggregates will

influence both the strength and the density of the concreteD

To sum up, as the volume of voids in a concrete increases,

both the strength and the density decrease, but the relation between

the strength and density will depend on the properties and proportions

of the aggregates and cement usedD

The relation between strength and density for various mixes,

when void content was varied by air entrainment, was found experimentally

and is presented in the following chaptersD

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3< SPECIMENS AND TEST PROCEDURES

3.1 General

Due to the number of parameters affecting both the strength

of concrete and its density, this investigation was 1 imited to the

consideration of two important variables, the total volume of air in

the concrete and the maximum size of aggregate.

The effect of changes In the volume of air vOids on both the

cyl inder strength and the density was examined. The volume of air voids

in the mixture was control led by adding an air entraining agent (Darex)

to the mixing water. Concretes with various mix proportions and three

different maximum sizes of aggregate were tested. Tables 1, 2, and

3 show the different batches and mixes with the corresponding number

of cyl inders made, mix proportions, amount of air entraining agent used

and the average density and compressive strength of each batch.

This investigation was broken up into three groups, according

to the maximum size of agg:egate used. The three groups were mortars,

concrete with 3/8 fnch maximum size coarse aggregate and concrete with

3/4 inch laxi~wm size coarse aggregaLe. There were two mixes in each

group, as 'rdic2ted in Tab1es '!~ 2) and 3.

T~e only variable in each mix was the amount of air entrain­

ing agent usedo

The procedure followed in preparing the test specimens is

described in the following sections of this chapter. Below is shown

a 1 ist of factors which were kept constant throughout the investigatlonu

They are:

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a) Mixer: 2 cubic feet capacity, Lancaster horizontal

pan mixer

_ b) Mixing ti!Tle~ 2t mInutes

c) Curing conditfons: moist room at constant temperature

d) Caps: on top only, liHydrocal l1 paste

e) Age at testing: 7 days

f) Cement: Type I I I Portland cement (high early strength)

g) Sand: Wabash river sand

h) Testing Machine: 300,000 pounds capacity hydraul ic press

i) Micrometer: used to measure a1 1 cyl inders (1/1000 inch

accu racy)

j) Scale: used to weigh all cyl inders (1/100 pound accuracy)

302 Materials and Test Procedure

All specimens were cast in 6 inch diameter by 12 inch cyl indri-

cal steel moldso The method fol lowed in making and testing the concrete

cyl inders was the same for all specimens of anyone mixo

3020 1 Aggregates

Three maximum sizes of aggregate were used: sand, 3/8 inch

gravel and 3/4 inch gravel 0 The fine aggregate was Wabash rIver sando

This was spread out and air-dried for more than 48 hours for the mortars,

but not for the concretes; however, in all mixes a water content test

I was performed for both the fine and coarse aggregates so that the total

I water content of the mix was always knowno All coarse aggregates used

were clean and roundo The sand was mainiy quartz and the gravel was

I mainly 1 imestone and dolomiteo The specific gravit ies of the aggregates

were measured fOl1owing A.SuT.oMo Standard Procedure C]27-59o

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sand: 2.62 grams per cubic centimeter

3/8 inch gravel~ 2065 grams per cubic cer.t.!meter

3/4 Inch g rtS 've 1 ~ 2056 grcms per cubIc centImeter

3.202 Cement

The cement used in 211 ffifxes was AoS.TcM. Type II ~ I Portland

cement. It W2S stored before :Jsing In a closed room to prever:t any

accumulation of moisture.

30203 Mixing

All the mixIng was done ~r. a Lancaster horizontal pan mixer

of two cubic feet capactty. The mixfng procedure was ider.tica1 for

all mixes.

The coarse aggregate (if required), sand and cement were

weighed to an accuracy of better than 1/4 pound. The mixer' was operated

for t to minute, until the dry materials were thcroughly mixedo

The water, weighed to an accuracy of 1/20 pound, and the

Darex, measured to 1/10 mill il iter, were mixed together and then added

to the dry ingredients. The concrete was then mIxed for 2 minutes.

A slump test was then taken followIng the A.S.T.M. Standard

Procedure CI43-58. The concrete from the slump test was returned to

the mixer and all the concrete mixed for another t minute. The speci­

mens were then prepared.

3.2.4 Compaction

Each batch was either hand-rodded or vibrated. The hand

rodding was done following the A.SoT.M Procedure C192-62T. The vibration

was done by introducing a mechanical 1 inch needle v~brator into the

cyl inders. All of the specimens of a single group were compacted by the

same met hod.

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3.2.5 Curing

All specimens were struck after 20 hours and placed in a moist

room for-a period of 6 days at a constant temperature.

3.2.6 Measurements and testing

On the seventh day, each cyl inder was measured and weighed

to obtain its density. Four readings of the diameter of each cyl inder

were obtained and two readings of its length. All cy1 inders were weighed,

on the same scale, when they were still moist. After this they were

capped with "Hydrocal" on the top surface, to obtain two smooth and

parallel surfaces, and were tested to failure under a compressive load,

in accordance with A.S.T.M. Standard Procedure C39-64.

An average diameter for each cyl inder was computed from the

four diameter readings; the average length of each·~ylirider, was also

computed. These two average readings were used to calculate the density

and the strength of the cyl inder. The average density and the average

strength for each batch is reported in Tables 1, 2, and 3.

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4. RESULTS

4.1 Results for Each Mix

The test results for each one of the six mixes presented in

Tables 1, 2 and 3 are shown in Figures 8 through 13. In these figures

each point represents one cy1 inder. The coefficient of 'variation in

strength for each of the mixes was computed and is shown in Table 4.

The deviation, in pounds per square inch, of anyone cyl inder from the

mean curve was measured in each figure and then used to compute the

coefficient of variation. It can be seen from Table 4 that the largest

value for the coefficient of variation of the test results is 5.5 percent,

for Mix E. The batches from this mix were made and tested in two

separate lots, but even so the standard deviation is relatively small,

indicating that the curves obtained are reasonably rel iable.

The slopes of the curves in Figures 8 through 13 give an indi-

cation of the sensitivity of the compressive strength of concrete to

changes in density. Since these 1 ines are curved, an arbitrary density,

near the maximum value, was chosen for each group to measure the slope

of each curve in the group. These densities and the corresponding slopes

are shown in Table 5. The slopes indicate that a 1 percent decrease in

density will cause a decrease of from 5 to 8 percent in strength.

I 4.2 Results for Each Group

j In Tables 1, 2 and 3 the average densities and average compressive

j strengths of the cyl inders in a batch are shown. The average values are

I plotted for each group in Figures 14, 15 and 16. These six curves are

the basis for the discussion of the results in each group.

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Figure 14 shows the test results for two mortars. Each of the

curves indicates that, for given mix proportions, type of aggregate and

water-cement ratio, the compressive strength of the mortar decreases as

the density decreases. From the slopes of the curves it can be seen that

a 1 percent error in density determination will cause an error of from

5 to 7 percent in strength.

The curve for Mix A has a smaller slope than that for Mix B;

it should be noted that it has larger water-cement and aggregate-cement

ratios. In other words, it is the leaner of the two mixes. This agrees

with the discussion of Walker and Bloem (12), who indicated that the

slope of a strength versus percent air curve will be steeper for a rich

mix than for a lean mix.

The difference in strength between mixes A and B at density

136 pounds per cubic foot was 23 percent.' This result may be used to

deal with the following practical problem~ One may wish to use the

strength-density relation for a given mix, say Mix B, to predict the I!

i strength of in situ concrete by measuring the density. If the mix

actually used were identical with Mix B~ a 1 percent error in density

measurement would give a 7 percent error in strength. If, however, the

mix on site were not identical with Mix B, but for some reason happened

to be identical with Mix A, an additional error of 23 percent would

result in the inferred strength, giving an error of 30 percent for a

percent error in density measurement. The difference in both water-

cement and aggregate-cement ratio for these mixes is 10 percent, which

I is greater than may be expected on a well-controlled job site. Whether

or not the total error in the inferred strength of the insitu concrete

I would be acceptable, depends on the circumstances of the job.

18

Figure 15 shows the results for M!xes C and D, for which

different mix proportions and water-cement ratios were used. The two

mixes, C and D, had water-cemenl ratios of 0.72 and 0.63 and aggregate-

cement ratios of 6.4 and 5.3, respectively. Both mixes had 3/8 inch

maximum size of aggregate.

Figure 15 shows that for g!ven mix proportions and water-

cement ratio, the compressive strength of the concrete decreases with

a decrease in density. The slopes of the curves were such that a 1

percent error in density determinatIon would cause about an 8 percent

error in the inferred strength.

From Table 2 it can be seen that Mix C had a higher aggregate-

cement ratio and higher water-cement ratio than Mix D. The curve i

corresponding to Mi~ C shows a sl ightly steeper slope than the curve for

Mix D but this is not signIficant within the 1 imits of experimental error.

It was found that the dIfference in strength for Mixes C and D

at the density 145 pounds per cubic foot was 5.5 percent. The two mixes

had differences of 13 and 20 percent in the water-cement and aggregate-

cement ratios, respectively. This indIcates that the strength-density

curve for one mix, say MIx C~ can be used to predict the strength of

another mix, say Mix D, with an accuracy of better than 14 percent, for

a 1 percent error in density determination.

Figure 16 shows the results for the two concrete mixes using

3/4 inch maximum size of aggregate. The two mixes, E and F, had water-

cement ratios of 0.57 and 0.66 and aggregate'-cement ratios of 5.5 and

5.4, respectively. Table 5 shows the slopes of the two curves. The

difference in the observed slopes for Mixes E and F is not significant,

19

withi n the 1 imlts of experimental error. These two curves show that

for a given mix, as the amount of a!r voids IS varied, the compressive

strength -decreases as the density of the hardened concrete decreases.

The slopes of the curves are such that a 1 percent change in density will

cause a change in strength of close to 7 percent.

The difference in strength between Mixes E and F at the

density 148 pounds per cubic foot was 4 percent. The two mixes had

differences of 15 and 2 percent in water-cement and aggregate-cement

ratios, respectively. The strength-density curve for one of these mixes

would predict the strength of the other mix within an error of 11 per­

cent, for a 1 percent error in density determination.

4.3 Results for All Mixes

Figure 17 shows a general trend of increase in the strength

with an increase in density. Various investigators (3), (4), (5:456),

ha v e i n d i cat edt hat the rei sag e ne r a 1 r e 1 a t ion 0 fin c rea sin g s t r eng t h

with density for 1 ightweight, high-density and no-fines concrete. This

general relation is also true for normal concrete.

The difference !n slope between the concretes with 3/8 inch

aggregate and the concretes with 3/4 Inch aggregate is small; a 1 percent

e r ro ;- i r de r') Sit Y mea sur em e n two u 1 d res u 1 tin a 7 to 8 per c en t err 0 r i n

strength for the two groups. The range of strength for all four concretes

at a density of 147 pounds per cubic foot is 22 percent. Therefore, for

the concretes with coarse aggregates here investigated, a single strength­

density curve may be used to predict the strength of a mix with an

accuracy of better than 30 percent, if the density measurement is in

error by 1 percent.

20

It i1. noteworthy that the resu"lts of Glanville, Coll ins and

Matthews (11), presented in Figure 6, show that a 1 percent error in

density determination "leads to an 8 percent error in the inferred

strength, which agrees well with the results obtained here for concretes

with both 3/8 and 3/4 inch maximum size of aggregateo

Mixes C, D, E and F, with coarse aggregates, covered a

larger range of water-cemer.t and aggregate-cement ratios than did the

mortars, Mixes A and Bo The overall error in strength which would be

obtained from a density measurement accurate to 1 percent, is 30 percent

for either the concretes or the mortars investigated hereo For a given

accuracy in strength determination a single strength-density curve would

therefore cover a larger rar.ge of concretes than mortarso

I I

21

50 CONCLUS IONS

_ Comparison of the densities of concr'ete cyl inders obtained by

weighing and measuring, and by the gamma ray method:. given in the Appendix

i n Fig u reA 9 and Tab 1 e A 3, show s t hat the den sit y 0 f a con c re t e s p e c i men

can be obtained non-destructively with an accuracy of better than 1 percent.

The coefficients of variation of the compressive strength,

relative to the plotted mean curves, are reported in Table 4 for the six

mixes. The maximum coefficient of variation was 5.5 percent; this was

for Mix E, which was made and tested in two lots in two different days.

Because the coefficients of variation are relatively low it can be con­

cluded that the test results are rel iable and reproducible.

The conclusions of this investigation are summarized below:

(a) The density of concrete was obtained non-destructively

using gamma radiation with an accuracy of better than 1 percent; most

readings were more accurate than t percent.

(b) The slopes of the strength-density curves, presented in

Table 5, indicate that for a given mix a 1 percent error in density

measurement would give rise to an error of 7 percent or less in the

inferred compressive strength for anyone mortar and 8 percent for any

concrete in the range tested. The latter result agrees with that of

Glanville, Col1 ins and Matthews (11).

(c) The relation between the compressive strength and density

for a given concrete m1x can be used to predict the strength of the con­

crete where a small variation in the water-cement ratio has occurred, due

for example to an error in workmanship. The error in strength for con­

cretes with one size of coarse aggregate, in the range considered here~

22

wo u 1 d be 1 e s s than 14 p e :- c e n t ) 1 f the dens r t y were m ea sur e da c cur ate -to 1 percent. The comparable error in strength for mortars considered

here would be 30 percent.

(d) A single curve :-elating the compressive strength and

the density of concretes with either 3/8 or 3/4 inch coarse aggregate,

in the range tested here, would give a strength estimate of any mix to

an accuracy of better than 30 percent, if the density were measured

accurate to percent.

(e) This investigation was carried out using entrained air.

The slopes of the strength-density curves for concretes were similar to

that obtained by Glanville, Col1 ins and Matthews (11), who varied the

amount of air by varying the compactive effort. The conclusions arrived

at here may therefore be assumed to be val id, however the air content

is varied.

I I I I

~ ~"" l.,.".",·.<,;i \i-'.J,l(>"~ ~ L_ .. -~':"J \",~t~~ ~

TABLE I

DETAILS OF MORTAR MIXES (GROUP 1)+

-----Air "t( -,':

Entraining Aggregate Water Number Agent to to Average Average

Batch of IIDa rex ll Cement Cement Density Strength Mix Number Cylinders -ml/lb of water- Rat i 0 (ale) Ratio (w/c) -1b/ft 3- -lb/in2-

A 6 0.05 5.0 0.70 135·9 3710

A 2 6 0.14 5.0 0.70 133.6 3L~70

A 3 5 O. J 9 5·0. 0.69 132.4 3450

A 4 4 0.38 5.0 0.69 130.7 3060

A 5 5 0.58 5.0 0.69 127·2 2820

A 6 5 0.77 5.0 0.69 126.8 2900

B 3 0.12 4.5 0.63 136.9 4850

B 2 5 0.30 4 (' . ) 0.63 135·3 4840

B 3 5 0.48 4.) 0.63 132.7 4100

B 4 5 0.60 4.5 0.63 131. I 3980

B 5 5 0.90 4 . ~) 0.63 128.9 3530 N w

+ Method of compaction by vibration

i: By weight

TABLE 2

DETAILS OF CONCRETE MIXES WITH 3/8: INCH MAXIMUM SIZE AGGREGATE (GROUP 2)+

Air * * Entraining Aggregate Water Number Agent to to Average Average

Batch of "Darex" Cement Cement Density Strength Mix Number Cy 1 f nders -ml/1b of water- Ratio (ale) Ratto (w/c) -lb/ft3- -lb/ln2-

C .5 0.24 6.4 0.72 144.8 ' 4270 '

C 2 5 0.48 6.4 0 .. 73 . 142.7 3640

c 3 5 0.67 . 6.4 0.71 139.3 3010

C 4 5 0.84 6.4 0.73 136.5 2540

C 5 5 1 .04 6.4 0.71 136.3 2450

D 5 0.0 5.3 0.63 147. 1 5200

0 2 4 0.23 5.3 0.63 144.7 ·4360

0 3 5 0.46 5.3 0.63 142.4 3870

0 4 5 0.69 5.3 0.63 140.8 3600

0 5 5 0.92 5.3 0.63 140.6 3700

+ Method of compaction by rodding

* By. weIght N +-

TABLE 3

DETAILS OF CONCRETE MIXES WITH 3/4 INCH MAXIMUM SIZE AGGREGATE (GROUP 3)+

Air * * Entraining Aggregate Water Number Agent to to Average Average

Batch of "Darex" Cement Cement DensljY Streng2h Mix Number Cy 1 i nders -ml/lb of water-· Ratto (a/c) Ratio (w/c) -1b/ft - -lb/ln .,.

E 9 0.0 5.5 0.57 150.0 4830

E 2 5 o. 14 5.5 0.56 148.3 4520

E 3 4 0.28 5.5 0.56 146.3 4280

E 4 8 0.42 5.5 0.57 144.2 4000

E 5 4 0.83 5.5 0.57 144.7 3970 E 6 5 1 .03 5.5 0.57 143.5 3540

E 7 5 0.70 5·S 0.56 t 41 .7 3460

F 5 0.0 5.4 0.66 148.7 4450

F 2 5 o. 12 5.4 0.66 147.9 4360

F 3 5 0.24 5.4 0.66 146.9 4150

F 4 5 0.48 5.4 0.66 144.9 3700

+ Method of compaction by roddlng N \J1

'* By weight

26

TABLE 4

COEFFICIENTS OF VARIATION OF CYLINDER STRENGTH

Coefficient of Number Variation of Strength

of Relative to Curve Group Mix Figure Cylinders (Percent)

Mortars A 8 31 4.3%

B 9 23 3.7

3/8 in. C 10 25 5.2 Aggregate

0 1 1 24 4.4

3/4 in. E 12 40 5.5 Aggregate F 13 20 3.6

I I

~~--~--

TABLE 5

SLOPES OF THE STRENGTH-DENSITY CURVES AT SELECTED DENSITIES

Group Hi x

Mortars

3/8 tn. Aggregate

3/4 in. Aggregate

A

B

C

o

--: E

F

Density at Which Slope is Q~oted

-lb/ft -

136.0

136.0

145.0

145.0

148.0

148.0

* To the nearest t percent.

Strength ~lope -klp/in2- -lb/in per lb/ft3-

3790 155 4850 255

4330 260

4590 250

4460 210

4310 225

Percent Change In Strength Due To a One Percent

Change In Density*

5.1 2

7

8t 8

7

7t

N

"

N c

........ 0..

..::L

:I: r-c..!) ::z: UJ 0:::: r-V'>

2.5

2.0

1 .5

1.0

~~ / 0

)0 l' ,,0 ,'u ,,,oey

V' R,' '1.\. @Z

/',~ ~~ ,/ /4~ ~'

.....-j 'J~ ,/ ~

.""

0 1:6 mix by vol ume -

o 1:7 mix by volume 0·5 t::. 1:8mix by volume • 1: 10 mix by volume

1 1 120 125 130

DENSITY OF 6 INCH CUBES - Ib/ft3

FIGURE 1. STRENGTH vs DENSITY FOR NO-FINES CONCRETE (From Mcintosh, et aI, Reference 6)

28

5.0

N C 4.0

......... a.

.::t. 3.0

::J: l-e.!) z: 2.0 t.LJ ex:: l-V')

1 .0

165

155 t"'f"\ ~ 4-......... .D

w 145 I-

LLJ ex:: u ::z: 0 u 1J.. 0

>- 135 l-

V')

::z: w c

125

SERIES 2G

,. Size of Aggregates O-No. 100 "V 0-1 in.

I a-No. 48 o 0-11 in. .... 'R. A a-No. 28 b. 0-2 in. -

-

0.08

~

~ ~~ Xi a-No. 14 I rregu 1 ar

~ ~ Grading

.-<;r O-No. 8 @ O-No. 4 .~ it!... 0 a-No. 4 @ 0-3/8 i ri.

'~ •• ~ r't

Q\ • 0-3/8 in. e 0-3/4 in •

~ ....,G1 + 0-3/4 in • ~ O-l± in. ....

~ ~ ~I ~ 'r

~ .11. !y-

I I --- ....., ,

o. 16 0.24 0.32 0.40

RELATIVE VOIDS IN CONCRETE - v

FIGURE 2. STRENGTH vs RELATIVE AIR VOIDS FOR SERIES 2G (From Talbot and Richart, Reference 10)

I 1 I

S'ERI'ES IZG I.

I I

Size of Aggregates ,. a-No. 100 "V 0-1 In.

I a-No. 48 o 0-lt in. ~ ~ ~-t a-No. 28 b. 0-2 in. ..

0.10

vd ~+, Irregular 17 :0: O-No. 14 P '\ 8! G radi ng

~, -9- a-No. 8 @ O-No. 4

"-L

~ 0 a-No. 4 (j 0-3/8 in.

"U\,j

~ • 0-3/8 in. e 0-3/4 in. !\-)

0-3/4 in. ® 0-lt in. l~~ +

liS

~ E9

~ ~ ~ ~): ~~ ~

-:u All "- • ",. -, I.

o • 20 0 • 3 a 0 • 40

RELATIVE VOIDS IN CONCRETE - v

FIGURE 3. DENSITY vs RELATIVE AIR VOIDS FOR SERIES 2G (From Talbot and Richart, Reference 10)

29 -~

-f--

~

~

----------

I

....,:..-.- .

t--

-t--

~

f--

~

:--

--

t

I

N c:

'" 0..

..:s:.

::r:: ..... <...!J Z L.LI 0:::: ..... V)

N c:

'" 0..

.:::l.

::r:: ..... <...!J z: UJ cr: ..... V)

5·0

4.0

3.0

2.0

1 .0

5~Q

4.0

3.0

2.0

1.0

30

" Nominal Values of ~ , • e = o. 15

.. . '" ~ • b- e = o. 1 Q

• • ::.. ~ 0 c = 0.06 ... .,

" ~ ............ ,

4-~~ ~

-...... ~~

"0

.1 ~ b- • 1\ ~ ./I. I'

p--"'!: '~ ~ ~ ::..~ " i'-c

L.;.,U- ~ --.. ~ r--~. ~ C ""' c -~ ~ ~ (") ~..-

OJ

O. 16 0.20 0.24 0.28

RELATIVE VOIDS IN CONCRETE - v

FIGURE 4. STRENGTH vs RELATIVE AIR VOIDS AT VARIOUS CEMENT CONTENTS

(From Talbot and Richart, Reference 10)

V·,···o.16 /~ J 1 J

/ Y ;. v =0.20

~/ ./ " I I I L-V /~ /~ v z:: 0.24

./ ~ ,/'

JV ./

/' v: " V ~

..,

V V V ~ '" ~

t:::-V

I

0.06 0.10 o. 15

RELATIVE VOLUME OF CEMENT - c

--

--

FIGURE 5. STRENGTH vs RELATIVE VOLUME OF CEMENT AT ~ARIOUS AIR VOIDS CONTENTS

(From Talbot and Richart, Reference 10)

[

I I 1 • I

a I-

~ ::I: I-<.!)

z lIJ cr: l-V')

1 .0 water/cement = 0.50 0.55 0.60 0.65 0.70

Ci) 6. 'V o-¢-0.8

0.6

0.4

0.2

0 0.75

Grad i ng A -Grading B - • A" 11).

0.80 0.85 0.90 0.95

DENSITY RATIO

FIGURE 6. RELATION BETWEEN STRENGTH RATIO AND DENSITY RATIO

1 • 0

(From Glanville, et al, Reference 11)

N 5·0 c

" 0-

.:x

3.0 ::I: .... <.!)

:z: L.tJ a:: I- 1.0 U')

6.5 6 ~ "'-.J I ~

5,05 r . f)-ro- f"...

"-""""""" r-c ~~ r.....

I I ""

'"t) ~ ~ 4.5 II - - r--.. r... .....

• Numbers indicate average cement

factors - 28 days I J I , I I I I I I

o 246 8

COMPUTED AIR CONTENT PERCENT BY VOLUME

10

FIGURE 7. STRENGTH vs PERCENT AIR AT VARIOUS CEMENT CONTENTS

(From Walker and Bloem, Reference 12)

31

~ .... - ~".

5.0

N c 4.0 "-a...

..:L

:r: l-e.!)

3.0 z W 0:: I-c.n

2.0

~ ~, 1'11'"",*1» 1£t''IIf'''., ~ """"""'" ~ ~ I!!I':'~ 111.1," If.', .. ~ I "'1',,, .. .,..,

,

~ ~

• • • --~

• .! - • ..

126

-- .----• •

128

• •

------~ •

130

•

132

DENSITY - 1b/ft3

134

FIGURE 8. STRENGTH vs DENSITY FOR MIX A

MIX A

alc = 5.0 w/c e 0.69 'air ::;zvarlable

6" by 12" cylinders 7 day strength

136

,

VJ N

~ ......., ~ ~~ ~ ~ ~"'···-·""·~1·'"

5.0 ./

N

4.0 c

C;X V • .. ~ • ..Jill. ,

a. .Y.

::r:

~ •

~ .-t!)

3.0 z w ~ .-"Vl

2.0

128 130 132 134 136

DENSITY - lb/ft3

FIGURE 9. STRENGTH vs DENSITY FOR MIX B

MIX B

a/c = 4.5 w/c = 0.63 air = variable

6" by 12" cyl inders 7 day strength

138

,

w w

---..-~-,~

5.0

N C

......... 4.0 0...

.::l.

:c I-(.!) Z lJJ 3.0 ex: I-Vl

V. • • J

~ ~ . .

~ ~ •

~ .",.

• 4

2.0

136 138 140 142 . 144

DENSITY - lb/ft3

FIGURE 10. STRENGTH vs DENSITY FOR MIX C

MIX C

a/c = 6.4 w/c = 0.72 air = variable

6" by 12" tyl inders 7 day strength

146

t

w +:-

~ -- __ I~'" .-w ~ t:tw~,<J ~ ~ ___ ____

N

4.0 c ........ Cl.

~

5.0 ~ v .

V 1

V .

:~

LP V

• It • ~ . .

~ •• :x: I- • • C,!) z

3.0 IJJ oc l-V) MIX D

ale = 5.3 wle = 0.63

2~0 air = variable

6" by 1211 cylinders 7 day strength

136 138 140 142 144 146 DENSITY - lb/ft3

FIGURE 11. STRENGTH vs DENSITY FOR MIX D

!

\.JJ \J1

5·0 ;

N C

......... 4.0 0..

..x

::c l-e.!) z UJ 3.0 oc l-(/)

2.0

138 140

I

~. AI"

~ ~.

• •

~ • • • •

.. A-.. .-"" •

~ ~ • ~ • • • •

MIX -E

ale = 5.5 wlc = 0.57 air = va r i ab 1 e

- 6" by 12" cylinders 7 day strength

142 144 146 148

DENSITY - lb/ft3

FIGURE 12. STRENGTH vs DENSITY FOR MIX E

I

\..oJ (j\

'5.0 \

N c 4.0 ....... 0..

.:::l.

:x: .-(!J

z 3.0 l1J cC .-V')

2.0

138 140

, • V-ee? • ,

~ ~

•

MIX F

ale = 5.4 w/e ::: 0.66 air - variable

" 6" by 12" eyl inders 7 day strength

142 144 146 148

DENSITY -, lb/ft3

FIGURE 13. STRENGTH vs DENSITY FOR MIX F

I I

I

VJ -......J

IftIIjJ ~ --,

5.0

N

c: 4.0 ........ 0.

.Y.

:x: .­<!J

r5 3.0 0:: .­en

2.0

128 130 132 134 136 138 DENSITY - lb/ft3

FIGURE 14. STRENGTH vs DENSITY FOR MORTARS

6

0

GROU'P 1 (Mortars)

Mix A

Mix B

\.N 00

iiiJ IIi«IW :~ •. _fl -.. .... li.,:",,,,J \if/~ ~ III!IW?'!!IIf ~ ~ ........-~""

5.0 \

I

N c 4.0

........ 0-

.::L

:x: .... ~

3.0 :z w 0:: .... Vl

2.0

/~ /"

~ 7 ~ V

~ / '-- c

.~

~ ~ GROUP 2

(3/8 in. gravel) --

D. Mix C

0 Mix 0

~.

136 138 140 142

DENSITY - Ib/ft3

144 148

FIGURE 15 •. STRENGTH vs DENSITY FOR CONCRETES WITH 3/8 INCH GRAVEL

,

I

w \.0

5.0

N C '4.0

......... a..

.:::L

:x: l0-t!) Z l1J 3.0 a:: t-V)

,',

2.0

140

..,.

~ V

~ ---'

~ ~ ~F

~

GROUP 3 (3/4 in. gravel)

0 Mix E

II Mix F

142' 144 146 148 DENSITY - lb/ft3

FIGURE 16. STRENGTHvs DENSITY FOR CONCRETES WITH 3/4 INCH,GRAVEL

1

,152

I I

.p­o

N C

....... 0-

.::t.

::c .­<.!J z: W o! .­Vl

5.0 I I I I r 7 0/0. ,

4.01 r --1---+178 y!-~~'+ __ + __ -LL a I 1;/ ~--vl A.C-/_--f---~ .. .A1'

3.0 I ::::;000-9 U I ft

2.0 1~------4--------+--------+--------r------~

126 130 134 138

DEN$ITY - lb/ft3

142

ALL MIXES

Group 3 (3/411 grave 1)

Group 2 (3/8" grilvel)

--- Group (Morta rs)

Each point is the average of each batch.

FIGURE 17. STRENGTH vs DENSITY FOR ALL MIXES

+-

I I I

42

LIST OF REFERENCES

1. Jones, R. Non-DestructIve Testing of Concrete, Cambridge University, University Press, Cambridge, London, 1962, 103 pp.

2. Preiss, K. "Measuring Concrete Density by Gamma Ray Transmission," Materials Research and Standards, Vol. 5, No.6, June 1964, pp. 285-291.

3 . Fe i sen he i s e r , E . I. and Wa s i 1, B. A. ' I H ea v y S tee 1 -A g g reg ate Con -crete," ACI Journal, Proceedings, Vol. 52, Sept. 1955, pp. 73-82.

4. Hanson, J. A. "Replacement of Lightweight Fines with Natural Sand in Structural Concrete," ACI Journal~ Proceedings, Vol. 61, July 1964, pp. 779-793.

5 . N e v ill e, A. M. Prop e r tie s 0 f Con ere t e , J 0 h n W i 1 e y & Son s, Inc., New Yo r k, 1963, 532 pp. p. 456, p. 216, p. 223.

6. Mcintosh, R. H., Balton, J. D. and Muir, C. H. "No-Fines Concrete as a Structural Material," Proceedings, Institution of Civil Engineers, London, Part 1, Vol. 5,. No.6, Nov. 1956, pp. 677-694.

7. Feret, R. "Societe D'Encouragement Pour L'lndustrie Nationale," Vol. 96, Series 5, 1897, p. 1604.

8. Feret, R. Etude Experimentale Du Ciment Arme, Paris, 1906, pp. 491-516.

9. Powers, T. C. liThe Physical Structure and Engineering Properties of Concrete," Portland Cement Assoc., Research Department Bulletin No. 90, Chicago, July 1958.

1 0 . Tal bo t, A. N. and Ric h art, F. E. liT h eSt r eng tho f Con ere t e : Its Relation to the Cement Aggregates and Water," University of III inois Engineering Experiment Station, Bulletin No. 137, Octo 1923, p. 10, p. 30, p. 33, p. 3 7, p. 64, p . 78.

11. Glanvi 11e, W. H., Call ins, A. R. and Matthews, D. D. liThe Gradi ng of the Agg rega tes and Workab i 1 i ty of Cone rete," Road Resea rch Technical Paper No.5, London, H.M.S.O., 1947.

12. Walker, S. and Bloem, D.· L. "Control of Quantity of Air Entrained in Concrete,1I National Ready Mix· Concrete Assoc., July 1950, 14 ppo

13. Walker, S., Bloem, D. L. and Gaynor, R. Strength to Maximum Size of Aggregate," Washington, Proceedings, Vol. 38, 1959.

"Relationships of Concrete Highway Research Board,

I I I I I

43

14. Walker, S. and Bloem, D. L. "Effects of Aggregate Size on Properties of Concrete," ACI Journal, Proceedings, Vol. 57, Sept. 1960. p. 283.

15. Gilkey, H. J. "Water-Cement Ratio Versus Strength: Another Look," ACI Journal, Proceedings, Vol. 57, April 1961.

16. Cordon, We Au and Gillespie, H. A. "Variables in Concrete Aggre­gates and Portland Cement Paste Which Influence the Strength of Concrete,1I ACI Journal, Proceedings, Vol. 60, Aug. 1963, p. 1029.

17. Bloem, D. L. and Gaynor, R. D. "Effects of Aggregate Properties on Strength of Concrete," ACI Journal, Proceedings, Vol. 60, Oct. 1 963, p. 1429.

18. Kaplan, M. F. IIF1exural and Compressive Strength of Concrete as Affected by the Properties of Coarse Aggregates," ACI Journal, Proceedings, Vol. 55, May 1959.

19. Singh, B. G. "Spec i f i c Su rface of A.gg regate Re 1 ated to Compress i ve Strength of Concrete and Flexural Strength of Concrete," ACI Journal, Proceedings, Vol. 54, April 1958, pp. 897-907.

20. Popovics, S. "An Investigation of the Unit Weight of Concrete;" Magazine of Concrete Research, Vol. 16, No. 49, Dec. 1964, pp. 211-220.

APPENDiX

MEASUREMENT OF CONCRETE DENSiTY USING GAMMA RADIATION

1. The Apparatus

Figure Al shows the apparatus. A source and detector of gamma

radiation are held on a U-frame so that the specimen may be placed

between them.

The source, 5 mill icuries of cesium-137, is held In a lead

shield. A hole in the shield permits a beam of gamma ray particles or

photons to move in the direction of the detector.

When the photons enter the concrete specimen, they may be

scattered or absorbed by atoms of the concrete, or may pass through the

r specimen without coll idingo The greater the density, the greater the

number of photons which suffer coll ision, the less the number of photons

I which strike the detector, and the lower the detected count rate.

Figure A2 shows a block diagram of the radiation detection

system. The detector is powered by the high voltage. When a photon

is detected a pulse is emitted which is passed to an ampl ifier and

then to a pulse height selector. The pulse height selector permits only

those photons within a preset height (cr ampl itude or voltage) range-to

pass to the scaler to be counted.

I The distribution of pulse heights observed with the apparatus

is shown in Figure A3. The peak is due to photons which do not coll ide

in the specimen, but are absorbed in the detector. The tail is due to

I photons which are scattered but not absorbed in the specimen or the

detector. If only the photons in the absorption peak are detected, then

I

I I

I

I I

I I

45

the geometrical resolution of the apparatus is improved, and a simple

cbrrection for the chemical composition of the concrete is possible (2).

The pulse height selector was therefore set to pass only those pulses

from 19.5 volts to 26.9 volts.

Due to the statistical nature of source decay, if two observa-

tions are made for the same time interval, they will not, in general, be

equal. If N counts are detected in T seconds, N is a norm.ally distri­

buted variate with a standard deviation of IN. The count should therefore

b~ large enough so that the coefficient of variation, 1//tJ, is sufficiently

small. For 6 inch concrete specimens the count rate with this apparatus

was approximately 1200 counts/second, so a 30 second counting time interval,

giving about 36,000 counts, was used.

2. Cal ibration

2.1 Theory of the Cal ibration Technigue

It has been shown (2) that the density with apparatus such as

this may be given by

p log (R /R)

e 0 (Al)

where R 0

is the count rate wi th no specimen in the apparatus

R is the count rate wi th the specimen in the appa ra tus

NA is Avogadrols cons ta nt

Z/A is the average rat i 0 of atomic number Z to atomic weight

A for the concrete

x is the path length of radiation in the specimen

is an experimenta11y determined value, which is constant

for a small range of specimen thickness and densityo

46

Homogeneous concrete cal ibration specimens are very difficult

to manufacture. Cal ibration was therefore carried out with 1 inch thick

slabs of aluminum, glass a~d lucite.

Table Al 1 ists the values of density p and Z/A, for the cal i-

bration specimens.

Figure A4 shows the values of ~ obtained, plotted against the

product (p x Z/A) for the four materials. The ordinate is plotted on

an expanded scale. It can be seen that ~ may be taken as constant to

within 1 percent over a range of approximately 20 percent in density p

or thickness x. The shape of the curves depends upon the apparatus

geometry and the setting of the pulse height selector.

2.2 Establ ishment of the Cal ibration Curve

Equation (Al) is rewritten for convenience as

p log. (R /R) eo'

(A2)

where 2Z/A is now defined as the chemical composition factor C.

The value of C was calculated for the ingredients of the

concrete used here from knowledge of the chemical compositions. Table

A2 1 ists the analyses, together with the computed values of C. It may

be observed from Table A2 that the value of C varies by no more than

0.2 percent for the dry materials, but is II percent different for water.

The factor C for concrete is, therefore, for all practical purposes, a

function only of the water content. This is plotted in Figure AS. It

may be observed that even an approximate knowledge of water content yields

an accurate value of C.

Cal ibration was performed on slabs; readings were taken on

cyl inders. The value of x in equation A2 was therefore taken to be the

I I i I

I I

47

diameter of the cyl inder mu1tipl ied by a correction factor, which was

the volume of the cyl inder "seenll by the beam divided by the volume

IIseen" in the slab, and was calculated from simple geometry. Figure A6

shows the result of an experiment which justifies this approach. Read-

ings were taken on slabs of both lucite and aluminum, and on acyl inder

of each. Equation A2 shows that the logarithm of the count rate is

inversely proportional to the density, at least over a small range.

Figure A6 shows that when the correction was appl ied to the diameters

of the cyl inders, the observed count rates did indeeed fallon the

straight log-l inear plot.

Substitutions of the fol lowing values in equation A2 yields

the cal ibration equation:

NA 0.60225 x 1024

x 0.993 x 2.54 x d, where d is the diameter of the cy1 inder

in inches

P 0.229 x 10-24

The cal ibration equation for 6 inch diameter cy1 inders is then

p 359" 0 log (R /R) C d e 0

(A3)

This equation is val id whatever the value of R ; for con­o

venience a standard value may be chosen. In this work it was 420,000

counts in 30 seconds, given a cal ibration equation of

p (A4)

where R is a count in 30 seconds and p is the density in pounds

per cubic feet.

48

The effect of the decaying strength of the source is removed

by taking the ratio R /R. The only effect of decay is then to require o

a longer_time to accumulate the counts required for accuracy. The half-

1 ife of Cs-137 is however 30 years, so that the 30 second time interval

need be increased by only I second every It years, to preserve the

same accuracy.

The background count rate was found to be less than the

standard error.f"N/T In the count rate determination; it was therefore

ignored.

The spatial resolution of the apparatus was determined by

taking a series of readings on lucite and aluminum slabs, as each was

moved laterally through the radiation beam. The results, plotted in

Figures A7 and A8, show that the end of the 4 inch slab had no effect

when itwas more than inch from the apparatus center-l ine giving an

effective diameter of 2 inches. Most of the count was, however, due

to the cent ra 1 linch of the beam.

3. Comparison of Densities by Gamma Ray and Weighing Methods

The densities of 23 concrete CYI inders were obtained by

weighing and measuring, and compared with densities obtained by using

the gamma ray apparatus.

Since concrete is a heterogeneous material it was necessary

to obtain a number of readings on the same cyl inder and calculate the

averaged density for the cyl inder. In this investigation ten readings

were taken on each cyl inder. Five readings were taken at two inch

intervals along each of two longitudinal 1 ines on perpendicular diameters.

The distance from the point nearest to the end of the cyl inder was greater

I f I , I

I I

49

than one inch, so that the apparatus "saw·· concrete over the full diameter

of the radiation beam. The diameter of the cyl inder was measured with a

micrometer at each point where a reading was taken with the gamma ray

apparatus.

To take a reading the cyl inder was placed on a small table

inside the U-frame, against the detector shield with its longitudinal

axis perpendicular to the 1 ine connecting the source and the center of

the detector. A visual check was made that the beam of radiation went

through a diameter of the cyl inder and not a chord. The ten points on

each cyl inder were placed in turn on the center 1 ine of the detector.

At each point a count was taken over an interval of 30.0 seconds.

To obtain the density of the concrete in the cyl inder, equation

A4 was used. Three factors were needed to calculate the density of the

material at each point, the count rate obtained from the gamma ray

apparatus in a period of 30.0 seconds (R), the diameter of the cyl inder

at a point where the count rate was taken (d), and the chemical com-

position factor (C) which was obtained from Figure AS knowing the ratio

of total weight of water to the total weight of dry material in the mix.

An average value of the calculated densities for the ten points in the

cyl inder was obtained. This average density was used as the density of

the concrete cylinder.

The densities obtained by the use of the gamma ray apparatus

in concrete cyl inders are compared with the densities obtained by

weighing and measuring in Table A3. For 20 out of 23 cyl inders the

error was less than t percent; for 1 cyl inder out of the 23 cyl inders

the error was greater than 1 percent.

50

Figure A9 shows a plot of the density obtained by weighing

and measuring the cyl inders against the density obtained with the gamma

ray apparatus. The two dashed 1 ines indicate a 1 percent deviation

between the two methods.

It can be concluded that an accurate value of the density of

concrete may be attained by the gamma ray apparatus used in this investi­

gation and described in this appendix.

51

TABLE Al

DENSITIES AND PARAMEltRS Z/A FOR THE CALIBRATION SPECIMENS

Density Materia 1 g/cc Z/A

Aluminum 2.700 0.4833

Glass 2.515 0.4969

Lucite 1. 184 0.5343

TABLE A2

I ANALYSES AND CHEMICAL COMPOSITION FACTORS C FOR

I THE COMPONENTS OF THE CONCRETE

Type III , Sand Gravel Cement Water (Percent) (Percent) (Percent) (Percent)

r Si02 54.20 38.46 20. 1 ~ A1 203 5.45 5.62 5.8

1 Fe203

2.40 3.42 2.2 f

1 MnO 0.02 0.05 0.24

I Ti02 0.01 0.01

CaO 15.65 18.96 63.6

MgO 3.63 9.37 2.8

I Ha 20 0.97 0.93

K20 1.04 0.88

j CO2 16. 14 22.09 1 .7 CaS0

3 3.2

I Factor C 0.9958 0.9948 '0.9962 1 .1093

I ~

52

TABLE A3

COMPARISON OF DENSITIES BY GAMMA RAY AND WEIGHING METHODS

Measured Dens i ty By -Cylinder Density Garmla Ray Deviation Percent

-lb/ft 3- -1b/ft3- -lb/ft3- Deviation

1 C1 136.5 136.4 -0. 1- -0.07 '.,

2 C1 136.4 136.0 -0.4 -0.29

3 C1 136.7 137.2 +0.5 +0.37

C2 135.0 134.5 -0.5 -0.37

r 2 C2 135.5 135.0 -0.5 - -0.37

3 C2 135.1 134.6 -0.5 -0.37 F

4 C2 135.7 135.5 -0.2 -0. 15

I 5 C2 134.4 134.7 +0.3 +0.22

1 C3 132.8 132.5 -0.3 .-0.23

( 2 C3 132.5 130.8 -1·7 -1.28 t 3 C3 132.4 132. 1 -0.3 -0.23

I 4 C3 132.8 132.3 -0.5 -0.38 ! 5 C3 132.3 132.2 -0. 1 -0.08

-; 1 C4 131 .0 130·7 -0.·3 -0.23 f- 2 C4 131 .4 131.0 -0.4 -0.30

3 C4 131 .0 130.6 -0.4 -0.31

I 4 c4 130.4 130.3 -0. 1 -0.08 5 C4 130.6 130.6 0.0 0.0

I 1 C5 129.7 128.9 -0.8 -0.62 2 C5 128.6 127·7 -0·9 -0·70 ,. 3 C5 129. 1 128.5 -0.6 -0.46

i 4 C5 129.3 128.8 '·0.5 -0.39

I 5 C5 128.2 127.6 -0.6 -0.47

I I

~ .... ... .'~f ..,..",. ~ p. ~:(( ;,~tJ} ~r'tlrp-;:,.

,... 22

Detector

Cable to spectromete,

Lead Shield

--~!f------~'+'~~~--~ ~'..L-\.;...' _-.-...... -.,.. ==-_______ --.J.

r--=.I I

Specimen

\' \

diameter round hole

U Frame

E to Q.)

co

c: -0

.fJ to

"'0 to

0:::

Source Lead Shield

FIGURE Al. DIAGRAM OF THE APPARATUS SHOWING A SPECIMEN IN POSITION FOR DETERMINING THE DENSITY

V1 W

... .-- ........ ....-

r-~---------------------------------,--~

I SPECTROMETER I I , I I HIGH PULSE I I VOLTAGE ---- AMPLIFIER ~ HEIGHT· :: . SCALER/TIMER

SUPPLY SELECTOR I I . I I I J -------------------------------------~

*

DETECTOR

FIGURE A2. BLOCK DIAGRAM OF THE DETECTION SYSTEM

V1 +-

-- .- ....-

....J c:( ::­a: UJ

~

..... -.J o ::-.

0:: t.LJ a..

Vl UJ Vl ....J ::::> a.. u. o a: LIJ CO 4 ::> Z

~ DETECTION CHANNEL I I .. --I

16000 I . I. I I A I I

I 12000 I 1\

8000 I L------~----~~------~------1-~~i_~,_tI----_j~'l---r~------~

4000 1< I • I I \:

4.0 8.0 12.0 16.0 20.0 24.0 28.0

PULSE HEIGHT - volts

FIGURE A3. DISTRIBUTION OF PULSE HEIGHTS OBSERVED

Vl Vl

N :E u

..:t N I 0

Ol

• 235 I I ',,_ ::;:a:;:~=o;>"()'""": "

.230

.225

• 220 I (I'

5 10 15 20 25 30

. p x l/A

FIGURE A4. (3 vsp x l/A

35 Vl 0'

~ ..... ...... 1I'!,.hi. IIftIP!'\IIW ~ I~"k<""" ~:t1""."f1f "'."..,.,... ............ ~

.. -'"

1 • 0 10 . .

u

0:: 0 ..... u « 1.008 lL.

z 0

t-V)

0 Q.. %: 0 1.006 u ..J « u :1: W' :r: u

1 .004

/

. / /

/ /

/ 0.08 0.10 0.12 o. 14 O. 16

WATER CONTENT (wt of water/wt of dry materIal)

FIGURE AS. CHEMICAL COMPOSITION FACTOR C vs WATER CONTENT

,

o. 18

V1 "-.J

I I I

I I

3.50

-3.40

3.30

3.20

4.00

3.90

3.80

58

-

'''" ~ Corrected diameter

I I I' I

~ / I I I I

~Actual diame~er I

~ I ALUM I NUM !II..

~ Diameter of cylinder c 4.511 in.

""- Corrected diameter = 4.48 in.

4.0 4.5 5·0

THICKNESS x

LUCITE

Diameter of cyl inder = 4.504 in.

Corrected di ameter ::: 4.44 in.

I d" I 1 , / ~ Corrected lameter

"- I I I I

" N V Actual diameter

"'-

~

4.0 4.5 5.0 6.0

THICKNESS x

FIGURE A6. LOG R vs THICKNESS x FOR ALUMINUM AND LUCITE

I

l­:z ::> o u

300,000

250,000

200,000

°

Slab

Center 1ine of detector

\ \

t1

~ -

1.0

e

\ ,} l) .... ~'

' .. -

...

2.0

59 Lead shield

Detector

•

~

j

J

... J 3.0 4.0

DISTANCE e FROM EDGE OF SLAB - inches

FIGURE A7. COUNT RATE R vs DISTANCE e FOR LUCITE

. u Go) CIl

"""

200,000

~ 150,000 c ~ o u

ex::

t­Z :::> o u

j

~

o

60

-

•

-

\.~ - ... ... - J -- -

1.0 2.0 ·3.0 4.0'

DISTANCE e FROM EDGE OF SLAB - inches F~GURE A8~ COUNT RATE R vs DIST~NCE e FOR ALUMINUM

IiW ~ ~ ..... ,~...;,i IJ'!Ifl'''''''' "'''!''""T0"'r'''J It 0"00';' .... r..>.T."77

(V'\

+J ~

'-. .0

V')

::J t-~ <l:: a.. a.. <J:

>-~

~ :l: <l:: c.!)

>-en

>-t-V')

z w 0

138

134

130

126

1% error

126 130 134 138 142

DENSITY BY WEIGHING AND MEASURING THE CYLINDERS 146

lb/ft 3 150

FIGURE A9. COMPARISON OF DENSITIES OBTAINED BY GAMt-1A RAY APPARATUS WITH DENSITIES OBTAINED BY WEIGHING AND MEASURING

0"'