ACI 214-77

7/17/2019 ACI 214-77

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ACI Committee Reports, Guides, Standard Practices, and Com

mentaries are intended for guidance in designing, planning, executing,

or

inspecting construction, and in preparing specifications. Reference

to these documents shall not be made in the Project Documents. If

items found in these documents are desired to be part

of

the Project

Documents, they should be incorporated directly into the Project

Documents.

ANSI/ACI

214 77

ACI

Standard

Recommended Practice for Evaluation of

Strength Test Results of Concrete A.CI

214

77 *

Reported y ACICommittee 2 4

V. M.

MALHOTRA

Chairman

V. RAMAKRISHNAN

HUBERT RUSCH

DWARD A. ABDUN·NUR

HOWARD

T.

ARNI

JOSEPH F. ARTUSO

ROBERT

M. BARNOFF

RICHARD J. DOERMANN

RICHARD

D.

GAYNOR

ARNOLD R. KLINE

K. R. LAUERt

ROBERTO

SANCHEZ.TREJO

ROBERT G. SEXSMITH

T. G.

CLENDENNING

HERBERT K. COOK

A.

M. NEVILLE

ROBERT E. PHILLEO

FRANCIS J. PRINCIPE

V. D. SKIPPER

J.

DERLE

THORPE

Statistical procedures provide valuable tools for assessing results of strength tests

and such an approach is also of value in refining design criteria and specifications.

The report discusses briefly

the

numerous variations

that

occur in the strength of

concrete

and

presents statistical procedures which are useful in interpreting these

variations.

Keywords: coefficient of

variation; compression tests; compressive

strength; concrete

construction;

concretes; cylinders; evaluation; quality control; s mpling; standard deviation; statistical analysis;

variations.

CONTENTS

Chapter 1 lntroduction 214-2

Chapter 2 Variations in strength 214-2

2.l-General

2.2-Properties of concrete

Chapter 3 Analysis of strength data

3.l-Notation

3.2-General

3.3-Statistical functions

Chapter 4 Criteria

4.l-General

4.2-Criteria for strength

requirements

4.3-Additional information

2.3-Testing methods

3.4-Strength

variations

3.5-Standards

of control

4.4-Quality control charts

4.5-Tests and specimens required

4.6-Rejection of

doubtful

specimens

214-3

214-7

Chapter 5 References 214-14

•

Adopted as

a

standard

of

the American Concrete Institute in

Aug -lst ~ 9 7 7

to

supersede

ACT 214-65

in

accordance

with the

Institute

s

standardIzation procedure.

tChairman during development of the

revision.

Copyright

©

1976 American Concrete Institute.

214-1

. All rights reserved including rights of reproduction and

use

m any form or by any means. including

the

making of copies

by. any photo "rocess,

or

by any electronic or mechanical device.

prmted

or wntten or

oral,

or recording for sound or visual

reproductIOn or

for

use m

any

knowledge

or retrieval

system

or de:Vlce

unle.ss

permISSIon In

wntIng

is

obtained

irorn

the

cOPYrIght

proprIetors.

-

7/17/2019 ACI 214-77


214-2

MANUAL

OF

CONCRETE PRACTICE

CH PTER

I INTRODUCTION

The

purposes

of

strength tests

of

concrete

are

to determine compliance

with

a strength specifica

tion and

to measure the variability of

concrete.

Concrete,

being

a

hardened

mass of heterogeneous

materials,

is

subject

to

the

influence of

numerous

variables.

Characteristics

of each of the

ingredi

ents of concrete, depending

on

their

variability,

may

cause

variations in

strength

of

concrete.

Variations

may also

be

introduced by

practices

used

in

proportioning,

mixing, transporting, plac

ing, and

curing.

In

addition

to the variations which

exist

in concrete itself, test strength

variations

will

also be introduced by the fabrication, testing, and

treatment of test specimens.

Variations

in the

strength of concrete

must

be

accepted, but con

crete of adequate quality can be produced

with

confidence

if

proper

control

is maintained, test

results

are properly interpreted,

and their

limi

tations are considered.

Proper

control

is achieved by the use of satis

factory

materials,

correct batching

and

mixing of

these

materials, correct batching

and mixing

of

sired

quality, and good practices in transporting,

placing,

curing, and

testing. Although the com

plex nature of concrete

precludes

complete

homogeneity, excessive variation of concrete

strength

signifies inadequate concrete controL

Improvement

in control

may permit a reduction

in the cost of

concrete

since the average strength

can be

brought

closer to specification require

ments.

Strength is

not necessarily

the most

critical

fac

tor

in

proportioning

concrete

mixes

since

other

factors,

such

as

durability,

may impose lower

water-cement

ratios

than are required to meet

strength requirements. In

such

cases, strength

will of necessity be in excess of structural de

mands. Nevertheless,

strength

tests are valuable

in such

circumstances

since, with

established

mix

proportions, variations in

strength are

indi

cative

of variations in other

properties.

Test specimens

indicate

the

potential rather

than the

actual strength of

the

concrete in a struc-

ture.

To be meaningful, conclusions

on

strength of

concrete

must

be derived from a pattern of tests

from which the characteristics of the

concrete

can

be

estimated with

reasonable

accuracy. Insuf

ficient tests

will

result in unreliable

conclusions.

Statistical procedures provide tools of consider

able

value in evaluating results of strength

tests

and information derived from

such

procedures

is

also of value in refining design criteria and speci

fications.

This

report briefly discusses variations

that

occur in the strength of concrete, and presents

statistical procedures that

are

useful in

the inter

pretation of these variations with

respect

to re

quired criteria and specifications. For these sta

tistical procedures to

be

valid, the data must be

derived

from samples

obtained

by

means of a

random sampling plan designed to reduce

the

possibility that choice

will

be

exercised

by the

sampler.

Random sampling means that

each

possible

sample

has

an

equal chance of being

selected. To insure

this

condition, the choice must

be

made by some objective mechanism such as

a table of random numbers.

f

sample batches are

selected by

the

sampler on

the

basis

of

his

own

judgment, biases are likely to be introduced

that

will

invalidate results

analyzed by

the procedures

presented here. Reference

1

contains

a discussion

of random

sampling

and a

useful

short table of

random numbers.

Additional

information

on the meaning

and

use

of this recommended

practice

is given in

Realism

in the pplication of CI

Standard

214-65.

2

This

volume

is a

compilation of

information

on ACI

214-65 that

was presented at

a

symposium held

at

Buffalo, N. Y, in 1971

In

addition to the papers

from

the symposium, it

includes

reprints of some

pertinent

papers

that were published

earlier in

the

ACI JOURNAL, and of discussion

that

resulted

from

them. Although the information

given was

based

on ACI

214-65, most

of

it is

still

relevant.

An additional source of

material

on evaluation of

strength

tests

is ACI Bibliography No.2, published

in 1960

3

CH PTER

2 VARIATIONS

IN STRENGTH

2.1-General

The

magnitude

of variations in the strength of

concrete test specimens depends on

how

well

the

materials, concrete

manufacture, and testing

are

controlled.

Differences

in

strength

can

be

traced

to two fundamentally different sources as shown

in Table 2.1: a) differences in strength-produc-

ing

properties

of the concrete

mixture

and in

gredients, and

b) apparent

differences

in

strength

caused

by variations inherent

in the test

ing.

2.2-Properties

of

concrete

t is

well

established that

strength

is governed

to a large extent by the water-cement ratio. The

7/17/2019 ACI 214-77


STRENGTH

TEST

EVALUATION

214-3

TABLE 2.I PRINCIPAL SOURCES OF

STRENGTH

VARIATION

Variations in the properties

of concrete

Changes in water-cement

ratio:

Poor control of water

Excessive variation of

moisture in aggregate

Retempering

Variations in water require

ment:

Aggregate grading ab

sorption particle shape

Cement and admixture

properties

Air content

Delivery time and

temperature

Variations in characteristics

and proportions of ingre

dients:

Aggregates

Cement

Pozzolans

Admixtures

Variations in transporting

placing and compaction

Variations in temperature

and curing

Discrepancies in testing

methods

Improper sampling

procedures

Variations due to fabrica

tion techniques

Handling and curing of

newly made cylinders

Poor quality molds

Changes in curing:

Temperature variation

Variable moisture

Delays in bringing cylin-

ders

t

the laboratory

i Poor testing procedures:

I Cylinder capping

Compression tests

I

first

criterion for producing concrete

of

constant

strength

therefore

is a

constant water-cement

ratio. Since the quantity

of

cement

and

added

water can be measured accurately the problem

of

maintaining

a

constant water-cement

ratio

is

primarily

one of

correcting

for the

variable

quantity

of free

moisture in

aggregates.

The

homogeneity

of

concrete

is

influenced by

the variability of the aggregates cement and ad-

mixtures

used since

each will contribute to varia

tions in the concrete

strength.

The temperature

of

fresh concrete influences

the

amount of

water

needed

to

achieve the proper consistency and

con

sequently contributes to strength variation.

Con

struction

practices

may

cause

variations in

strength

due to inadequate

mixing poor

com

paction delays

and improper

curing. Not

all

of

these are reflected in specimens

fabricated

and

stored under standard

conditions.

The use of admixtures adds another factor since

each admixture adds another variable to concrete.

The batching

of

accelerators retarders

pozzolans

and air-entraining

agents must be

carefully

con

trolled.

2 3 Testing methods

Concrete tests mayor may not include all the

variations

in strength

of

concrete

in

place de

pending

on

what

variables

have been introduced

after

test specimens were made. On the other

hand discrepancies in sampling fabrication cur

ing

and

testing

of specimens may cause indica

tions

of

variations in strength which do

not exist

in

the

concrete in

the

structure. The project

is

unnecessarily penalized

when

variations from this

source are

excessive. Good

testing

methods

will

reduce

these variations and standard testing

procedures such

as

those described

in

ASTM

standards

should be

followed

without

deviation.

The importance

of

using

accurate testing ma

chines and

producing

thin

high-strength

plane

parallel caps

should

need

no

emphasis

since test

results

can be no

more accurate than the

equip

ment and

procedures

used.

Uniform t st results

are

not

necessarily accurate t st results Lab

oratory

equipment

and

procedures should

be

cali

brated

and checked periodically.

CHAPTER

3 ANAlYSIS

OF

STRENGTH DATA

3.1 Notation

fo

n

R

factors for computing within-test

standard deviation from average range

required average

strength

to

assure

that

no more than

the permissible propor

tion of tests

will fall

below

specified

strength

specified strength

number of

tests

range

maximum for

average

range used

in

control charts for moving average for

range

R

t

average range

standard deviation

within-test

standard deviation

batch-to-batch

standard

deviation

a

constant multiplier for standard

de

viation

a) that

depends on the

number

of tests expected

to fall

below

fo

coefficient

of

variation

within-test coefficient of variation

an

individual

test result

average

of

test results

7/17/2019 ACI 214-77


214-4

5

(/)

-

(/)

W

10

-

o

w

CD

::J

Z

169

183

197

MANUAL OF CONCRETE PRACTICE

211

225

kgf/cm2

239

x-

I

I

253

95.45 %

267

281

295

309

k- ------

-2 () - - - - - --:: <- --

--

------ -2()-

-

-->-1

1

I

1

I

1

68.27

I

1 r = - - - - ) - - - - - - T - - - - - ) - - - - - ~ 1

I 1 I 1

323

1 I 0 I

1 I I

I 1

0

I

)=

462psi

32.5kgf/cm2)

V=

13.2 1

I 01 0 0 I

I 01 0 0 0 I

0

1

0 0 0 10

o o

o

o

o

o o

o

o

o

o o

o

o

COMPRESSIVE

STRENGTH

PS

I

1

1

1

1

1

1

1

1

Fig.

3.3(a)-Frequency

distribution of strength data and corresponding normal distribution

3.2-General

To

obtain

maximum information, a sufficient

number

of tests should be

made

to indicate the

variation

in the concrete produced and to permit

appropriate statistical procedures to be used in

interpreting the

test

results. Statistical procedures

provide

the best

basis

for

determining

from such

results

the

potential

quality

and

strength of the

concrete

and for

expressing

results in the

most

useful form.

141

(): .

34

p i

(23.9

kof/cm2

Compressive strength, psi

Fig.

3.3(b)-Normal

frequency curves for different stand

ard deviations

3.3-Statistical functions

The

strength of concrete test specimens on con

trolled projects can

be

assumed

to fall into a

pattern similar

to the normal

frequency

distribu

tion

curve

illustrated in Fig.

3.3

(a).

Where there

is good control, the strength

values will

be

bunched

close to

the

average,

and the curve will

be

tall and

narrow. As

the

variations in

strength

increase, the values spread and the curve be

comes

low

and elongated, as illustrated by

the

idealized curves shown

in

Fig.

3.3 (b). Because the

characteristics of such curves

can be

defined

mathematically,

certain

useful

functions of the

strength can

be calculated

as follows:

3.3.1 Average

X-The average strength of all

individual tests

x

= Xl + X

2

+

X3

+

...

+

n

n

(3-1)

Where Xl, X

2

Xs n are the strength results

of individual tests

and n

is

the

total

number

of

tests made. A test is defined as the average

strength

of

all specimens

of

the

same

age fabri

cated

from

a

sample

taken

from

a single batch of

concrete.

3.3.2

Standard

deviation a-The

most generally

recognized measure of dispersion is the root-mean

square

deviation of

the strengths from their

average. This statistic is known as the

standard

deviation

and may

be considered to be the radius

of

gyration

about the line of symmetry of

the

7/17/2019 ACI 214-77


STRENGTH TEST

EVALUATION

214·5

area under the curve of the frequency distribu

tion of

strength

data,

such as that

shown

in Fig.

3.3 a). The

best

estimate of cr based on a

finite

amount of

data,

is obtained by Eq. (3-2), or by

its algebraic equivalent, Eq. (3-2a). The

latter

equation is preferable

for

computation purposes,

because it is not only simpler and more adaptable

to

desk

calculators,

but it

avoids

the

possibility of

trouble due to rounding

errors.

or

() = { Xl - X)2 +

X2

- X)2 +

Xu

- X 2]/n - 1}%

• /

~ X . 2

_ ~ X i )

V

n

a= n 1

(3-2)

(3-2a)

3 3 3 Coefficient of variation, V :The standard

deviation expressed

as a

percentage of

the

v e r ~

age

strength is

called

the coefficient of variation:

a

V = X 100

X

(3-3)

3.3.4 Range,

R-Range is the statistic

found

by

subtracting

the lowest

of

a group of numbers

from

the

highest one

in the group. The

within-test

range is

found by

subtracting

the lowest

of

the

group

of cylinder

strengths averaged

to produce

a

test

from the

highest of

the group.

The within

test

range

is

useful

in

computing the within-test

standard deviation

discussed

in

the following sec

tion.

3.4-Strength

variations

As mentioned previously, variations

in

results

of strength

tests can

be

traced

to two

different

sources: (a) variations in testing methods

and

(b) properties of

the

concrete mixture and in

gredients.

It is possible by

analysis

of

variance

to compute the variations attributable

to

each

source.

3 4 1

Within-test

variation - The variation in

strength of

concrete

within

a single test is found

by computing the

variation of

a

group of

cylinders

fabricated from a sample of concrete

taken

from

a

given

batch. It is reasonable to

assume

that a

test sample of

concrete

is homogeneous and any

variation

between

companion

cylinders

fabricated

from a given sample is caused by fabricating,

curing, and testing variations.

A

single

batch of

concrete,

however, provides

insufficient data

for

statistical

analysis

and

com

panion cylinders from at least ten batches of con-

TABLE 3.4.I-FACTORS FOR COMPUTING WITHIN

TEST

STANDARD DEVIATlON

Number of

specimens

d

2

1/d2

2

1.128

0.8865

3

1.693

0.5907

4 2.059 0.4857

5

2.326

0.4299

6

2.534

0.3946

7

2.704

0.3698

8

2.847

0.3512

9

2.970

0.3367

10

3.078

0.3249

From Table

B2, ASTM

Manual

on Qual i ty

Control of Ma-

terials Reference 4

crete are required to establish reliable values

for

R. The

within-test

standard deviation

and

coef

ficient of variation can be

conveniently computed

as follows:

where

1/d

2

V

1

X

01

=

d

2

R

V

1

= a1 X 100

X

= within-test

standard deviation

(3-4)

(3-5)

a constant depending on

the

number of

cylinders averaged to

produce

a test

Table 3.4.1)

average

range within groups

of com

panion cylinders

= within-test

coefficient of

variation

= average strength

3 4 2 Batch-ta-batch

variations-These variations

reflect

differences

in strength which

can

be at

tributed to variations in

(a) Characteristics

and

properties

of

the in

gredients

(b) Batching, mixing,

and sampling

(c) Testing

that

has not been detected from

companion

cylinders since

these tend

to

be

treated

more alike

than cylinders tested at

different times

Fig.

3.4.2 al-Approximate

division of

the

area

under

the normal frequency distribution curve

7/17/2019 ACI 214-77


214-6


The batch-to-batch

and

within-test

sources of

variation are related

to

the

overall

variation

[Eq. 3-3)] by the following expression:

3-6)

50

60

Q;

>

J

70

0

c

Cii

C

80

e:

'"

.=

c

'

90

;

Q;

ro

Ol

95

e:

0

c:

Q

u

Q;

0..

Percent

of average strength

Fig. 3.4.2 bJ-Cumulative distribution curves for different

coefficients of variation

98.4

84.4 70.3

50

60

70

....

80

J

i

....

CIt

-

90

II:

CD

U

....

95

D

Q..

96

97

98

99

1400

1200

1000

where

o = overall standard deviation

01 =

within-test

standard deviation

02 = batch-to-batch standard deviation

Once

these parameters have been computed,

and

with the

assumption

that the results

follow a

normal frequency distribution curve, a large

amount

of information

about the test results

be

comes known. Fig. 3.4.2 a)

indicates an

approxi

mate

division

of

the area

under the

normal

frequency distribution curve.

For example,

ap

proximately 68 percent

of the area

equivalent

to

68 percent of the test results) lies within ± 10 of

the average, 95 percent within ± 20 , etc. This

permits

an

estimate

to

be

made of the portion of

TABLE 3.4.2-EXPECTED PERCENTAGES OF

TESTS

LOWER

THAN f

WHERE

X

EXCEEDS

fa BY

THE

AMOUNT SHOWN

Average

Expected

Average

Expected

percentage

percentage

strength,

of

strength,

of

X

low tests

X

low

tests

fo

+ 0.10a

46.0

f + 1.6a

5.5

fo

+ 0.20a

42.1

fo + 1.7a

4.5

fo

+ 0.30a

38.2

fo

+ 1.80

3.6

fo + 0.400

34.5

fo

+ 1.9a

2.9

f,, + 0.50a

30.9

fo + 2.0a

2.3

fc + 0.60a

27.4

fo + 2.10

1.8

fo

+ 0.700

24.2

fo + 2.2a

1.4

fo + 0.80a

21.2

fo

+ 2.3a

1.1

f + 0.90a

18.4

fo

+ 2.4a

0.8

f

+ 0

15.9

fo +

2.50

0.6

fo

+ 1.10a

13.6

fo

+ 2.60

0.45

f

+ 1.200

11.5

fo

+ 2.70 0.35

f

+ 1.30a

9.7 f + 2.8a 0.25

fo

+ 1.400 8.1 fc + 2.90

0.19

fo + 1.500

6.7

fo + 3.00

0.13

I

kgf/cm2

56.2 42.2

28.1

14.1

o

---_::::::.

800 600

400 200 o

Compressive

strength-psi

below average

Fig.

3.4.2 cJ-Cumulative

distribution curves for different

standard

deviations

7/17/2019 ACI 214-77


STRENGTH

TEST EVALUATION

214 7

T BLE

3.5 5T

ANDARD5 OF CONCRETE CONTROL

Overall variation

Standard deviation for different control standards, psi kgf/cm2)

Class of operation

Excellent

I

Very

good

I

Good

I

Fair

I

Poor

General

construction

below 400

400 to 500 500 to 600

600

to

700

above 700

testing

28.1) 28.1) 35.2) 35.2) 42.2)

42.2) 49.2)

49.2)

Laboratory trial

below 200 200

to

250 250

to

300

300

to

350

above

350

batches

14.1)

14.1) 17.6) 17.6) 21.1)

21.1) 24.6)

24.6)

Within-test variation

Coefficient of

variation

for differe nt control standards,

percent

Class of operation

Excellent

I

Very

good

Field

control testing

below 3.0 3.0

to

4.0

Laboratory trial

batches

below 2.0 2.0 to 3.0

the test results expected to fall within given

multiples

of

of

the

average

or

of

any

other spe

cific

value.

Table 3.4.2

has been

adapted from

the

normal probability integral of the

theoretical

normal

frequency

distribution

curve and

shows

the probability

of

tests falling below to in terms

of

the average strength

of

the mix X· = f r

(to +

ta . Cumulative distribution curves can

also

be plotted

by

accumulating the

number

of

tests below any given strength

expressed as a

percentage of the

average strength for different

coefficients of variation or

standard

deviations.

Fig. 3.4.2

b) and

3.4.2 c)

present such

informa

tion.

In

these

figures,

the ordinate indicates the per

cent of the population

of

strength values which

may be expected

to

exceed

the

strength

indicated

by any abscissa

value

for a

selected

coefficient of

variation or standard deviation.

I

Good

I

Fair

I

Poor

4.0

to

5.0

5.0

to

6.0

above 6.0

3.0 to 4.0 4.0 to 5.0

above 5.0

3.5 Standards of

control

The

decision as to whether

the standard

devia

tion or the coefficient

of

variation

is

the appro

priate measure

of

dispersion

to

use

in

any given

situation depends on which

of

the two

measures

is

the

more

nearly constant

over

the

range of

strengths

characteristic

of

the particular situation.

Present information indicates that the standard

deviation

remains

more

nearly constant

par

ticularly

at

strengths over

3000 psi 211

kgf/cm

2

.

For

within-test variations the coefficient of

varia

tion

is

considered

to be

more applicable

see Ref

erences

5-10).

Table

3 5 shows the variability that can be ex

pected

for compressive strength tests on projects

subject to different degrees of control.

These

values

are

not

applicable to

other strength

tests.

CHAPTER

4 CRITERIA

4.1 General

The

strength

of control cylinders

is generally

the only tangible evidence of the quality of

con

crete

used

in

constructing

a structure. Because of

the possible disparity between the strength

of

test cylinders and the load-carrying capacity of

a

structure

it is unwise

to place

any

reliance

on

inadequate

strength data.

The

number

of tests lower

than

the desired

strength

is

more important

in

computing the

load

carrying

capacity of concrete

structures

than

the

average strength obtained. t

is

impractical,

how-

ever, to specify

a

mmlmum strength

since

there

is

always the

possibility of

even

lower

strengths,

even when control

is good.

t

is also recognized

that

the cylinders may

not accurately

represent

the concrete in each portion

of

the structure. Fac

tors

of safety are

provided

in design

equations

which

allow for

de v i a t ion s

from

specified

strengths

without jeopardizing the safety

of

the

structure. These have been evolved on the basis

of

construction

practices, design procedures,

and

quality

control techniques used

by

the

construc

tion industry.

t

should

also

be remembered

that

for

a

given

mean strength,

if

a

small

percentage

7/17/2019 ACI 214-77


214-8


1.50

_0

'

~ 1 . 4 5

..<::

Chance of strength being

lower

than

specified

g, 1.40

; - - - - - - - - - /

1;; I 35

0 .

Q)

1.30 ---- --

5l

:;

1.25

c;,

I. 20 + - - - - 1 - J - I - ~ _ ¥ _ - ~ ~ + _ _ -

~ 1.15

::>

CT

.:: 1.10

o

o

1.05

5

10 15

Coefficient

of

variation, percent

20

25

Fig. 4.1

(aI-Ratio

of required average strength

fer to

specified strength

fe

for various coefficients of variation

and chances of falling below specified strength

of the test results fall

below

the design strength,

a corresponding large percentage of the test re

sults will be greater than the

design

strength

with

an equally

large

probability of being

located

in a critical area. The consequences of a localized

zone of low-strength

concrete

in a

structure

de

pend on many factors; included

are the

probability

of early overload,

the

location and

magnitude

of

the low-quality

zone in

the structural unit, the

de

gree

of

reliance

placed

on strength in

design,

the

initial

cause of

the

low

strength, and the

conse

quences,

economic and

otherwise,

of structural

failure.

The

final

criterion

which

allows

for

a certain

probability of tests falling below fo used in design

is a designer's decision based on his intimate

knowledge of the

conditions

that are

likely

to

prevail. Building Code Requirements for Rein

forced Concrete (ACI 318-71) , provides guide

lines in this regard, as do other building codes and

specifications.

To

satisfy strength

performance

requirements

expressed in this

fashion

the

average

strength

of

concrete must

be

in excess of

fe ,

the design

strength.

The amount of

excess

strength depends

on

the expected

variability

of test results as

expressed

by a coefficient of variation

or standard

deviation,

and

on

the allowable proportion of low

tests.

Strength

data

for

determining the

standard

deviation or coefficient of variation should rep

resent

a

group

of

at least

30 consecutive

tests

made

on concrete

produced

under

conditions similar to

those to be expected on the project. The require

ment

for

30

consecutive

strength

tests will

be

con-

kgf/cm

2

0

14.1

70.0

£

1000. . ; . r : ; : . . r r T: : . . . ; . . r : : . . . . . . : . . ;

70.0

g.

(I I

-c 8 0 0 t - - - - - + - + - - - , A - - - - - t 7 L - - - + - ~ _ _ _ l 5 6 . 2

C1l

~

·0

C1l

~ ~ o 6 0 0 r _ - - + - ~ - + _ ~ - ~ ~ r _ _ + - - - ~

»

... 42.2

OlE

~ ~

~

0>

~ ~

-b

g'

+- 4 0 0 r _ - - - - - , 1 t - - - - . - - + _ - r - - ~ - - - - + - _ _ : 7 _ l 2 8 . 1

~

(I I

-c

·3

2oot---- -t-7L---b----r --- -----i 14.1

cr

-

(I I

(I I

C1l

U

)

W

O ~ ~ ~ ~ ~ ~ 0

o 200

400

600

800

1000

Standard dev iation, psi

Fig. 4.1

(bl-Excess of

required average strength cr

to

specified strength

fa

for various standard deviations and

chances of falling below specified strength

sidered to have been complied with

if the

tests

represent either

a group of 30

consecutive

batches

of

the

same class of

concrete or the

statistical

average for two groups totalling 30 or more

batches. Similar conditions

will be difficult to

define and

can be

best

documented

by

collecting

several groups of 30 or more tests. In general,

changes in materials and procedures will have a

larger

effect

on the

average

strength level than

on

the

standard deviation or coefficient of varia

tion.

S

i g n i f i

can

t

changes generally include

changes in type and brand of portland cement, ad

mixtures,

source

of aggregates,

mix proportions,

batching, mixing, delivery, or testing.

The

data

should represent concrete produced to meet a

specified

strength

close to

that

specified

for the

proposed work, since the standard deviation may

vary

as

the

average strength varies. The

required

average strength

fer

for any

design

can be

com

puted

from Eq. (4-1) or (4-1a) ,

(Table

3.4.2), or

approximated from Fig. 4.1 (a) or 4.1 (b), depend

ing

on

whether the

coefficient of variation

or

standard

deviation

is used.

where

fer

fe =

t

f

fa

r

=

(1 -

tV

fer

=

fo

+ a

required average strength

design strength specified

(4-1)

( 4-1a)

a constant depending upon the proportion

of tests

that may fall below fe (Table

4.1)

forecast

value of

the

coefficient of varia

tion expressed as a fraction

forecast

value

of

the

standard

deviation

7/17/2019 ACI 214-77


STRENGTH

TEST EVALUATION

214-9

kgf/cm2

4

169

197

225

253

28

309

337

366

394

20

j)

Vi

15

<t-

o

-

c

10

U

L

Q)

0..

5

Compressive Strength, psi

Fig. 4.1 c)-Normal frequency curves for coefficients of variation of

10 IS,

and 20

percent

Whenever the average of a

certain

number of

tests

n is involved in the specif ication, Eq. 4-1)

is modified as follows:

and

fe

fer =

t

In

for = fe ta

In

4-1b)

4-1c)

Fig.

4.1

c) demonstrates

that

as

the

variability

increases

fer

must increase and thereby illustrates

the economic

value

of good control.

The requirement

of

at least

30

test results men

tioned

previously is

based on the fact that

25

to

30 randomly selected test results from a

normally

distributed population provide estimates

of

the

population average and standard deviation that

can

be

used

as

the population

values.

f only

a

small number of results is available on which to

base

estimates,

then

the

values, especially for

standard

deviation,

are unreliable, and

there is no

way in which

fer

can be

determined

so

that

a

specific

percentage of future tests will

be above

fe ,

assuming that the present

test results are

the

only

information available.

f previous information exists for concrete

from

the

same

plant

meeting

the

similarity require

ments described

above,

that

information

may be

used in deciding

on

a

trial value

of

a

to be

used

in

determining the target

fer.

TABLE 4.I-VALUES OF

t

Percentages

of tests

falling

within the

Chances

of falling

limits X ± ta

below

lower limit

40

50

60

68.27

70

80

90

95

95.45

98

99

99.73

3

in

10

2.5

in

10

2

in

10

1 in 6.3

1.5

in

10

1 in 10

1 in 20

1

in

40

1 in 44

1 in 100

1 in 200

1 in 741

0.52

0.67

0.84

1.00

1.04

1.28

1.65

1.96

2.00

2.33

2.58

3.00

For small

jobs

that

are

just

getting started,

where

no

prior

information is available,

the

con

crete

should be designed to produce an average

strength

fer

at

least

1200 psi 84.4 kgf/cm2)

greater

than

fe . As

the job

progresses and

more

strength

tests

become available, all

the strength

tests can

be analyzed together to give a more reliable esti

mate of the standard deviation, and Eq. 4-1),

4-1a), 4-1b),

and

4-1c)

can be used

to

calculate

a less conservative fer.

4.2-Criteria for strength requirements

The amount by which the average strength of

a

concrete mix fer should exceed fe depends

on

the

criteria

used in the

specifications for a par

ticalar

project.

The

following

are

examples of

calculations

that

would

have

to

be

made

to select

7/17/2019 ACI 214-77


214-10

MANUAL OF

CONCRETE

PR CTICE

the design strengths of

a

mix

that

will

meet the

requirements

of a

particular

code or specification.

4.2.1

Criterion No l -A stated

maximum

pro-

portion of random individual strength

tests

that

will

be permitted to

fall below fo on the average.

ASTM

C 94-74 uses a similar

approach.

For con

crete in

structures

designed

by the ultimate

strength method, ASTM recommends

that

not

more than 10 percent of

the

strength tests have

values

less than the

specified

strength fe .

As an

example, consider

the situation

where no

more than 1

in

10

random

individual

strengths

will be permitted to be

below

an fo of 4000 psi

(281

kgf/cm2).

Standard deviation method

Consider

very good quality

control

as indi-

cated by a

standard deviation

of 450

psi

31.7

kgf/cm

2

. Using Eq. 4-1a) and Table

4.1,

we have

fer

= fo + tu

= 4000 + 1.28 X

450

=

4580 psi 322 kgf/cm2)

As a result, for a

structural

design strength

fa

of 4000 psi

(281

kgf/cm

2

), the

concrete mixture

should

be proportioned

for

an average

strength

of

not less than

4580

psi 322

kgf/cm

2

).

Note that

the coefficient of variation is 450/4580) X

100

=

9.8

percent.

Coefficient of variation method

Consider

good quality

control

as indicated by

a coefficient of variation of

10

percent.

Using

Eq.

4-1) and Table 4.1,

we have

f

fo

cr =

1 - tV

_

fo

fer

- 1 - 1.28 0.10)

= 1.15 fo [see also Fig. 4.1 a)]

= 4600 psi 324 kgf/cm

2

)

Using this

approach

and this data

the

concrete

mixture

should

be proportioned

for an average

strength of

not

less than 4600 psi 324

kgf/cm2).

4.2.2 Criterion No 2-A certain probability

that

an average of

n

consecutive strength

tests

will be

below

fo .

ACI

318-71

suggests

that after

sufficient

test

data become

available

from a

project,

the fre-

quency

of occurrence of averages

of three con

secutive tests below

f

should

not

exceed

1 in 100.

As

an example, consider the

situation

where

no

more

than

1 in

100

of

averages

of three consecu

tive strength tests

will

be permitted to be

below

an fa of

4000

psi (281

kgf/cm2).


Consider

a

standard deviation

of 750 psi (53

kgf/cm

2

.

Using Eq. 4-1c) and Table 4.1, we have

tu

fer =

fo +

In

= 4000 psi

+

2.33 750)

J3

= 5000 psi 351 kgf/cm2)

As a result, for a structural design strength fe

of 4000 psi (281

kgf/cm

2

, the concrete

mixture

should

be proportioned

for

an average strength

of

not

less

than

5000

psi

351

kgf/cm

2

.


Considering

a coefficient of variation of

15

per-

cent

and

using Eq. 4-1b)

and

Table 4.1, we

have

fo

fer

-

1 _

tV

In

4000

- 1 _ 2.33

(9.

15 )

J3

= 5000

psi

351 kgf/cm

2

Using this

approach the concrete

mixture

should be proportioned for an average

strength

of not less than

5000

psi 351

kgf/cm2).

4.2.3 Criterion No

3 -A

certain probability that

a random individual strength test will be more

than a certain

amount

below f0 .

This

approach is also

used

in

ACI

318-71 by

stipulating

that

the probability of

a

random test

result

being

more than 500 psi 35.1 kgf/cm

2

)

below

fo should be 1 in 100.

As an example, consider a probability of 1 in

100 that a strength test

will

be more than

500

psi 35.1 kgf/cm2)

below

an

fo

of

4000 psi (281

kgf/cm2) .

Standard deviation

method

Considering a

standard

deviation of

750

psi

(53 kgf/cm2) and using Eq. 4-1a) and Table 4.1,

we have

fer =

fe

- 500 + ta

=

4000 -

500

+ 2.33 750)

= 5245

psi 369

kgf/cm

2

)

As a

result

the

concrete

mixture

should

be

pro-

portioned

for an

average strength of

not

less than

5245 psi 369

kgf/cm2).

Coefficient

of

variation

method

Using

Eq. 4-1)

and

Table

4.1,

and a coefficient

of

variation

of

15 percent,

we

have

fer

fo

- 500

tV

4000 -

500

1 - 2.33 0.15)

5390

psi 379

kgf/

cm2)

Using this approach,

the

concrete

mixture

should be proportioned for an

average

strength

of

not less than

5390

psi 379 kgf/cm2).

7/17/2019 ACI 214-77


STRENGTH

TEST

EVALUATION

214 11

TABLE 4.3 EVALUATION OF ONSE UTIVE LOW STRENGTH

TEST

RESULTS

1

2

\

3

I

4 5

Averages less

than

indicated

Probability of

averages less

require

investigation

than

fc ,t

Number of

percent

consecutive

Criteria for original

selection

of fer

tests

averaged

1 test in 100

1 test

in

10

less than

below

fe

[tc - 500 psi

(35.2 kgf/cm2] 1 test in 10

below

f

For

V =

15,

percent

For given 0

For

given

0

1

0.86f/

fe - 0.770

fo - 500

+

0.760 10.0

2

0.97fo

fe

-

0.170

f

- 500

+

0.880 3.5

3

1.02fo

fo

+

0.100 fe - 500

+

1.140

1.3

4

1.05f/

fe

+

0.260 fe - 500

+

1.300

0.5

5

1.07f/

fe +

0.360

fe -

500

+

1.410

0.2

6

1.08fo

fo

+

0.440

fe

-

500

+

1.490 0.1

The probability of averages less

than the

levels

indicated is approximately

2

percent i f the

population average equals f

and the standard

deviation or coefficient

of variation is at the

level

assumed.

t f the population average equals fer and the standard deviation

or coefficient

of variation

is

at

the level assumed.

4.2.4 Criterion No. 4 A certain probability that

a

random

individual strength test will

be

less than

a certain percentage of

f t

As an example consider a probability of 1 in

100 that a

strength test will be

less than

85 per

cent of an

fc

of

4000

psi (281 kgf/cm2).


Using

Eq. (4-1a)

and Table

4.1

and

a

standard

deviation

of 750 (53 kgf/cm

2

, we have

fc

0.85 fc + ta

=

0.85 (4000) + 2.33 (750)

=

5145

psi

(361 kgf/cm2)

As a result the concrete mixture should be pro

portioned

for an

average strength of

not

less than

5145 psi (361 kgf/cm

2

.


Using Eq. (4-1) and Table

4.1

and a coefficient

of

variation of

15

percent, we have

fer

=

0 85f/

tV

0.85 (4000)

1 -

2.33

(0.15)

5230 psi (368 kgf/cm2)

Using this approach,

the

concrete

mixture

should be proportioned for an average strength of

not less than 5230

psi

(368 kgf/cm

2

) •

4.3 Additional information

Table 4.3

presents additional information. The

values in the body of

the

table in Columns

2,

3,

and

4

are the

strength

levels below

which

in

dividual

tests or

averages of different

numbers of

tests should not

normally fall.

These

values are

based on the premise that the

concrete is pro

portioned

to produce

an average strength

equal

to fer The values in Column 2 are theoretically

correct

only

for

concrete

with a coefficient of

variation of 15

percent. Those

in

Columns

3

and

4 apply to any known

standard

deviation.

In

either

case

the

probability

of

their

being

exceeded

when the

concrete

is

properly controlled

is only

about

0.02.

Thus,

failure to

meet

the tabulated

limits

in

a larger proportion

of

cases

than that

stated

may

be an indication

that the

current

average strength is less than fer or that ) or V

has

increased. This could

be

caused

by

lower

strength

or poorer control than expected, or both. The

possibility

should

not be

overlooked

that

the low

tests

may

be caused

by

errors in

sampling or

test

ing rather than deficiency in the

concrete

itself.

In

any case,

corrective action

is

warranted.

Column

5

shows

the

probability

that

the average

of any

given

number of consecutive

tests

will

fail

to equal

or

exceed fe if the concrete is

propor

tioned to produce an average strength equal to

fel t can be seen that

increasing

the number of

tests

to be averaged increases the likelihood

that

fe will

be

exceeded since variations

tend

to

bal

ance out

with

an increased

number

of tests in a

set. For enforcement purposes, it is appropriate

and

logical to select the number of consecutive

tests

to

be

averaged in

such

a way that the ac

ceptance

level

is equal to

f t

This would mean an

average

of three

consecutive tests for concrete in

which

one

out

of

ten tests would be

permitted

to

be lower than f/ t should,

however,

be remem-

7/17/2019 ACI 214-77


214-12


bered

that,

according to the statistical theory as

sumed in the derivation of the values,

such

fail

ures

may

be

expected

by chance alone one time

in 50 even if the

concrete

is

controlled

exactly

as anticipated and is

overdesigned

to yield an

average

strength

equal to f r

Most specifications for concrete strength require

that a test

be

comprised of two

or

three specimens

from

the same sample of concrete. The

specimens

are

necessary

to

obtain

a

reliable average

for

a

given sample and to

provide

range data R for

determining within-sample

variations.

4.4 Quality control charts

Quality

control charts

have been used by

manu

facturing industries for

many

years

as an

aid

in

reducing variability and increasing efficiency in

production. Methods are well established for

the

setting

up

of such

charts

and

are outlined

in

con

venient form in the STM

Manual on Quality

Control of Materials

4

Based on the pattern of

previous

results and limits

established

therefrom,

trends become

apparent

as soon as

new

results

are

plotted. Points which fall outside the calculated

limits indicate that something has affected the

control

of the process. Such charts

are recom

mended

wherever

concrete

is in

continuous pro

duction over considerable periods.

Three

simplified charts prepared specifically

for concrete control are

illustrated in Fig. 4.4.

Required

overage

strength

fcn

.-

4000

J)

a .

\

o \

o \

_.L

-

:E

While these

do

not

contain

all

the features of

formal control

charts they

should

prove useful to

the engineer,

architect,

and plant superintendent.

a) A chart in which the results of all strength

tests

are

plotted as received. The

line for

the

re

quired

average strength is established

as

indicated

by

Eq. 4-1a) or Table 4.3

and the

specified

design

strength.

b)

Moving

average

for compressive

strength

where the

average is plotted for

the

previous five

sets of

two

companion cylinders for each day

or

shift, and the specified

strength

in this case is

the

lower

limit.

This

chart is valuable in

indicat

ing trends and will

show the

influence of seasonal

changes,

changes

in

materials,

etc. The

number

of

tests

averaged to

plot

moving averages with

an appropriate lower limit

can be

varied to suit

each job.

c) Moving average

for

range where the

average range

of

the previous

ten

groups

of com

panion cylinders is plotted each

day

or shift. The

maximum average range allowable for good lab

oratory control

is also

plotted. Maximum

average

range

is

determined

as discussed in

Section

4.5.

Fig. 4.4

shows

Charts a), b), and c)

for

46

tests.

To

be

fully effective

charts

should

be main

tained throughout

the

entire

job.

280

~ 3 0 0 0 - - - ~ - - - - ~ ~ ~ ~ ~ - - - - ~ ~ - - ~ - - ~ ~ ~ - ~ ~ - - - - 2 1 0

. /

v;

Specified strength fc _

o

l)

:;; 2000

Required strength

=

f + to-

J)

~ = = = = = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

a . Movi ng average

for strength

Each point average strength

u 4000 of

five

previous test groups

3000

300

l)

0>

C

o

a::

100

o

Required average strength, f

cr

-

_____

_

______

L

Moving

average

for range

~

Average

range for two cylinders : .0564 fer

Average ra nge tor three

cylinders

=0846

fer

4

8

12

6

20

24 28

32

Each

point

average of

ten previous

ranges

36

40

44

Sample numbers

Fig.

4A--Quality control charts for concrete.

48

210

2

7

7/17/2019 ACI 214-77


STRENGTH TEST

EV LU TION

214 13

4.5 Tests and specimens required

For

any

particular

job, a

sufficient

number of

tests

should

be

made to insure accurate represen

tation of the variations of the concrete.

Concrete

tests can be made either on

the

basis of

time

elapsed

or

cubic yardage

placed

and conditions

on each job will determine the most practical

method

of

obtaining

the number

of tests needed.

A test is

defined

as the average

strength

of all

specimens of the same age fabricated from a

sample

taken

from a

single batch

of concrete.

A project

where

all concrete operations are

supervised

by

one engineer

provides

an excellent

opportunity for control and for accurate estimates

of reliability with a

minimum

of tests.

Once

op

erations are

progressing

smoothly tests

taken

each

day or shift, depending

on

the volume of

concrete

produced,

are

sufficient

to obtain data which re

flect the variations in the concrete of the

struc

ture.

In

general,

it

is

advisable to

make

a

sufficient

number of tests so

that

each different type of con

crete placed during anyone day will be repre

sented by at least one test which is an average

of

two standard 6 x 12 in. cylinders tested at the

required age. Single specimens

taken

from

two

different batches each day will

provide

more re

liable information

on overall

variations,

but it is

usually desirable to make companion snecimens

from the same sample to obtain a

check

on the

within-test variation.

The

number of specimens required by the en

gineer (architect) should be based

on established

standards

but may

be reduced as

the

reliabilities

of

the producer, the laboratory, and the contrac

tor are established.

The

laboratory has

the

responsibility of making

accurate

tests,

and

concrete

will

be penalized un

necessarily

if tests show greater variations or

lower average strength

levels

than actually exist.

Since the range between companion specimens

from the

same sample

can be assumed

to

be

the

responsibility of

the

laboratory, a control

chart

for ranges Fig. 4.4) should be maintained by the

laboratory

as a

check on

the

uniformity

of its

operations.

I t

should

be noted

that

these

ranges

will not reveal day to day differences in test

ing, curing, and

capping

procedures

or

testing

procedures which

affect strength levels

over long

periods. The range between companion cylinders

depends on the

number of

specimens in

the

group

and the within-test variation. This relationship is

expressed

by the following equation [see Eq. 3-4)

and 3-5)]

4-2)

where m is

the

average range in Control Chart

c)

of

Fig. 4 4

The within-test

coefficient

of

variation

V

should not be

greater

than 5

percent

for good

control (Table

3.5), and the estimate of

the

corresponding average range will

be:

m =

0.05 X 1.128) f r

= 0 05640fer

for groups

of two

companion cylinders

m

= 0.05 X 1.693)

f r

=

0 08465fer

for groups

of three

companion

cylinders.

A cylinder of

concrete

6 in. in diameter and 12

in. high

which

has

been moist cured for

28

days

at 21 C is generally considered a

standard

speci

men for strength

and

control of concrete

i f

the

coarse aggregate does not

exceed

2 in. in nominal

size. Many times,

particularly

in

the early stages

of

a job, it becomes

necessary

to

estimate

the

strength of

concrete

being produced

before

the

28-day

strength

results are available. Concrete

cylinders from the

same

batch should

be

made

and tested at 7 days, or at

earlier ages utilizing

accelerated test procedures.

The 28-day strength

can

be estimated by extrapolating early test

data.

The strength of

concrete

at later ages, particu

larly where

a pozzolan or

cement

of

slow

strength

gain is used, is more realistic

than

the

standard

28-day strength. Some

structures

will not be

loaded

until

concrete has

been

allowed to mature

for

longer

periods

and advantage can be taken of

strength

gain after

28 days. Some

concretes

have

been found to produce

at

28 days less than 50

percent of their ultimate strength.

I f

design is

based on

strength at later ages, it becomes neces

sary to correlate these strengths with

standard

28-day

cylinders

since

it

is

not practicable

to use

later

age specimens

for

concrete

acceptance.

I f

possible,

the correlation should be

established

by

laboratory tests before construction starts. I f

mix

ing plants are located in one place for long enough

periods,

t

is

advisable to

establish

this

correlation

for reference even though later age concrete is

not immediately involved.

Curing concrete

test

specimens

at the

construc

tion site and

under

job conditions is sometimes

recommended since this is considered more rep

resentative of the curing

applied

to the structure.

These

special tests

should not

be confused with,

nor replace, standard

control

tests.

Tests

of

job

cured specimens

may be highly

desirable

and

are

necessary when determining

the

time of

form

removal, particularly in cold weather, and when

establishing

the strength of steam-cured

concrete

pipe, block,

and

structural

members.

The potential strength and variability

of

con

crete can be established by

standard

6 x

12

in.

cylinders made and cured

under standard

condi

tions. Strength

specimens

of

concrete made

or

cured under other than standard

conditions pro

vide

additional information

but

should

be analyzed

and reported

separately.

7/17/2019 ACI 214-77


214-14

MANUAL

OF CONCRETE PRACTICE

4.6 Rejection

o doubtful specimens

The practice of

arbitrary rejection

of test cylin

ders which

appear too far out of line

is

not

recommended since the normal pattern of

proba

bility establishes the possibility of such results.

Discarding tests

indiscriminately

could seriously

distort the strength distribution, making analysis

of

results

less reliable.

t occasionally happens that

the

strength

of one

cylinder

from

a

group made from

a

sample devi

ates so far

from

the mean as to

be

highly im

probable. t is

recommended

that a

specimen from

a

test

of

three

or

more specimens be discarded if

its deviation from

a test

mean

is

greater

than

3a and

should

be

accepted with

suspicion

if its

deviation

is

greater than

2a. f

questionable varia

tions

have been observed during fabrication, cur

ing

or testing of

a specimen,

the specimen should

be rejected. The test average should be

computed

from the remaining

specimens.

A

test (average of all specimens

of a

sample)

should

never be rejected

unless

the

specimens

are

known to

be faulty,

since it represents

the

best

available

estimate

for

the sample.

CHAPTER 5 REFERENCES

1. Natrella,

M.

G. Experimental Statistics, Hand-

book No.

91

U. S. Department of Standards, National

Bureau

of Standards, Washington, D. C. 1963 p p. 1-4

to 1-6.

2. Realism in

the

Application

of

ACT Standard 214-65

SP-37, American Concrete Institute, Detroit, 1973

215

pp.

3.

Evaluation

of

Strength

Tests of Concrete,

ACI

Bibliography No.2, American Concrete Institute,

De

troit, 1960

13

pp.

4. ASTM Manual

on Quality

Control

of Materials

STP 15-C American Society for Testing and Materials,

Philadelphia,

Jan.

1951 127 pp.

5. Neville,

A. M.

The Relation Between Standard

Deviation and Mean Strength of Concrete Test Cubes,

Magazine

.of

Concrete Research

(London),

V. 11 No.

32 July 1959 pp. 75-84.

6.

Metcalf,

J. B. The Specification of Concrete

Strength, Part

II The

Distribution

of

Strength of

Concrete for Structures in

Current Practice, RRL Re -

port No. LR 300 Road Research Laboratory, Craw

thorne, Berkshire, 1970 22

pp.

7. Murdock, C.

J.

The

Control

of

Concrete Quality,

Proceedings

Institution of Civil Engineers (London),

V. 2 Part I July 1953 pp. 426-453.

8. Erntroy, H. C. The Variation of Works Test

Cubes,

Research

Report

No. 10

Cement

and

Concrete

Association,

London,

Nov. 1960 28 pp.

9.

Rusch,

H. Statistical Quality Control of

Concrete,

Materialpriifung (Dusseldorf), V. 6 No. 11 Nov. 1964

pp. 387-394.

10. Tentative Recommended Practice for Conduct

ing

an Interlaboratory

Test

Program

to

Determine the

Precision

of

Test Methods

for

Construction

Materials,

(ASTM

C 802-74T), 1975

Annual

Book of ASTM Stand-

ards Part

13

American

Society for

Testing and Ma

terials,

Philadelphia, pp. 414-443.