aci code

1. This document has been approved for use by agen-
cies of the Department of Defense and for listing in the
DOD Index of Specifications and Standards.
Recommended Practice for Evaluation of Strength
Test Results of Concrete (ACI 214-77)*
(Reapproved 1997)
Reported by ACI Committee 214
V. M. M A L H O T R A
Chairman
EDWARD A. ABDUN-NUR RICHARD J. DOERMANN V. RAMAKRISHNAN
HOWARD T. ARNI R I C H A R D D. GAYNOR HUBERT RUSCH
JOSEPH F. ARTUSO ARNOLD R. KLINE ROBERTO SANCHEZ-TREJO
ROBERT M. BARNOFF K. R. LAUER? ROBERT G. SEXSMITH
T. G. CLENDENNING A. M. NEVILLE V. D. SKIPPER
HERBERT K. COOK ROBERT E. PHILLEO J. DERLE THORPE
FRANCIS J. PRINCIPE
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; sampling; standard deviation; statistical analysis;
variations.
CONTENTS
Chapter I-Introduction ......................................................2
Chapter 2-Variations in strength .............................................2
2.1-General
2.2-Properties of concrete
2.3-Testing methods
Chapter 3-Analysis of strength data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1-Notation 3.4-Strength variations
3.2-General 3.5-Standards of control
3.3-Statistical functions
Chapter 4-Criteria . . . . . . . . . . . . .
4. l-General
4.2-Criteria for strength
requirements
4.3-Additional information
Chapter 5-References . . . . . . . . .
. . . . .
. . . . .
4.4-Quality control charts
4.5-Tests and specimens required
4.6-Rejection of doubtful specimens
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
*Adopted as a standard of the American Concrete Institute in August 1977, to super-
cede ACI 214-65, in accordance with the Institute’s standardization procedure. This
recommended practice for evaluation of strength test results has been developed from
data derived from tests performed on concrete limited to a compressive strength of 6000
psi or less.
Whairman during development of the revision.
C%.@yyrightl976, American Concrete Institute. All rights reserved including rights
of reproduction and use in any form or by any means, including the making of copies by
any photo process, or by any electronic or mechanical device, printed, written, or oral,
or recording for sound or visual reproduction or for use in any knowledge or retrieval
system or device, unless permission in writing is obtained from the copyright
proprietors.

2. CHAPTER 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. If 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 Application of ACI Standard 214-65? 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.s
CHAPTER 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
It is well established that strength is governed
to a large extent by the water-cement ratio. The
2 ACI STANDARD

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 to the laboratory
Poor testing procedures:
Cylinder capping
Compression tests
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-
CHAPTER 3-ANALYSIS
3.1-Notation
da and =
lldz
fcr =
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
fc’ =
-
x =
En =
STRENGTH
specified strength
number of tests
range
maximum for average range used in
control charts for moving average for
range
TEST EVALUATION
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 may or 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 test results
are not necessarily accurate test results. Lab-
oratory equipment and procedures should be cali-
brated and checked periodically.
OF STRENGTH DATA
=
=
--
--
--
--
--
--
=
average range
standard deviation
within-test standard deviation
batch-to-batch standard deviation
a constant multiplier for standard de-
viation (0.) that depends on the number
of tests expected to fall
coefficient of variation
within-test coefficient of
an individual test result
average of test results
below f:
variation
3

4. kgf /cm2
199 183 197 211 225 239 253 267 281 295 209 323
I I I I I I I I I I I I
I
I68.27%
r=---r------
I
T
_----c--_--4
I
C O M P R E S S I V E S T R E N G T H P S I
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.
kgf/cm2
I 169 197 225 263 261 309 337 366 394 4
I I I I
I I I I I
Q s 340 PSI (23.9 kgf/c.m2)
T= 550 psi (39.4 k&b?-)
2000 2400 2600 3200 3600 4000 4400 4600 5200 5600 6(
1
Compressive strength, psi
Fig. 3.3(b)-Normal frequency curves for different stand-
ard deviations
4 ACI STANDARD
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
j&x1+x2+x,+...+x,
n (3-1)
Where X1, X2, X3 . . . X, 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

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 CI, 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.
o= (E(Xl--)2+ (x,-x)2+...
+ (Xn - X)2]/n - l}fh (3-2)
or
G=
d~xi” - (CXi)'
n- 1
(3-2a)
3.3.3 Coefficient of variation, V-The standard
deviation expressed as a percentage of the aver-
age strength is called the coefficient of variation:
v = + x 100 (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 3.4.1 l-FACTORS FOR COMPUTING WITHIN-
TEST STANDARD DEVIATION*
Number of
specimens
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
d-2 l/CL
*From Table B2, ASTM Manual on Quality 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
Cl =
l/d2 =
R =
VI =
X =
01 = -j-R (3-4)
2
VI = g x 100 (3-5)
within-test standard deviation
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-to-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
34.1%
1 Q.
Fig. 3.4.2(a)-Approximate division of the area under
the normal frequency distribution curve
STRENGTH TEST EVALUATION

6. The batch-to-batch and within-test sources of
variation are related to the overall variation
[Eq. (3-3) ] by the following expression:
o2 = 012 + 022 (3-6)
7 0 8 0 9 0
Percent of average strength
46.0 fc’ + 1.60
42.1 fc’ + 1.7
38.2
34.5
30.9 2.3
27.4 1.8
24.2
fe’ + 0.800 21.2
f: + 0.90
k;’18.4
1 fc’ + 0 15.9
018
13.6
11.5
p;
* 0:25
0.19
fc’ + 1.50 f0’ + 3.0 0.13
-
Fig. 3.4.2(b)-Cumulative distribution curves for different
coefficients of variation
where
G = overall standard deviation
o1 = within-test standard deviation
o2 = 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 3t la of
the average, 95 percent within t 20, etc. This
permits an estimate to be made of the portion of
TABLE 3.4.2-EXPECTED PERCENTAGES OF TESTS
LOWER THAN &’ WHERE x EXCEEDS f: BY THE
A M O U N T S H O W N
Average
strength,
x
Expected
perceo;ltage
low tests
Average
strength,
X
Expected
percztage
low tests
kgf/c&
8 4 . 4 70.3 56.2 4 2 2 28.1 14.1 0
6 0
8 8 0
s
&
z 90
ce
$j 9 5
e 9 6
9 7
1400 1200 1000 8 0 0 6 0 0 4 0 0 2 0 0 0
Compressive strength-psi below average
Fig. 3.4.2(c)-Cumulative distribution curves for different standard deviations
ACI STANDARD

7. TABLE 3.5-STANDARDS OF CONCRETE CONTROL
Overall variation
Class of operation
General construction
testing
Laboratory trial
batches
Standard deviation for different control standards, psi (kgf/cmz)
Excellent Very good Good Fair Poor
below 400 400 to 500 500 to 600 600 to 700 above 700
(28.1) (28.1) (35.2) (35.2) (42.2) (42.2) (49.2) (49.2)
below 200 200 to 250 250 to 300 300 to 350 above 350
(14.1) (14.1) (17.6) (17.6) (21.1) (21.1) (24.6) (24.6)
Within-test variation
Class of operation
Coefficient of variation for different control standards, percent
Excellent Very good Good Fair Poor
Field control testing
Laboratory trial
batches
below 3.0 3.0 to 4.0 4.0 to 5.0 5.0 to 6.0 above 6.0
below 2.0 2.0 to 3.0 3.0 to 4.0 4.0 to 5.0 above 5.0
the test results expected to fall within given
multiples of 0 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 f: in terms
of the average strength of the mix x = fcr =
(fO’ + to). 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.
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/cm2).
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 ever, to specify a minimum strength since there
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. It is impractical, how-
is always the possibility of even lower strengths,
even when control is good. It 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 deviations 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. It should also be remembered that
for a given mean strength, if a small percentage
STRENGTH TEST EVALUATION

8. Coefficient of variation, percent
Fig. 4.1 (a)-Ratio of required average strength fc,. to
specified strength fc’ for various coefficients of variation
Fig. 4.1(b)-Excess of required average strength f, to
and chances of falling below specified strength
specified strength fc’ for various standard deviations 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 ft 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 (AC1 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 f6, 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.
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 c a n 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 fcr for any design can be com-
puted from Eq. (4-l) or (4-la), (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.
fc’
fw= (1 - tv) (4-1)
fcr = fc’ + to (4-1a)
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-
where
fcr =
fc’ =
t =
v=
CT=
required average strength
design strength specified
a constant depending upon the proportion
of tests that may fall below fJ (Table 4.1)
forecast value of the coefficient of varia-
tion expressed as a fraction
forecast value of the standard deviation
8 ACI STANDARD
kgf/cm*
Standard deviation, psi

9. kgf/cm2
141 .I 69 197 225 253 281 309 337 366 3
I”“1 ’ ” ’ ” ” ” ”
2400 2800 3200 3600 4ooo 4400
Compressive Strength, psi
5200
Fig. 4.1(c)-Normal frequency curves for coefficients of variation of 10, 15, and 20 percent
Whenever the average of a certain number of
tests TZ is involved in the specification, Eq. (4-l)
is modified as follows:
fer= -$
l--Z=
Vn
(4-lb)
and
fcr = fc’ + toV n
(4-lc)
Fig. 4.1 (c) demonstrates that as the variability
increases fcr 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. If 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 fcr can be determined so that a
specific percentage of future tests will be above
f’ assuming that the present test results are the
o’nly information available.
If 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 c to be used in
determining the target fcr.
TABLE 4.1-VALUES OF t
Percentages of tests
falling within the
limits X * to
40
50
6680.27
;:
;8
95.45
98
ii.73
-
Chances of falling
below lower limit
-
. -
t
3 in 10 0.52
2.5 in 10 0.67
2 in 10 0.84
1 in 6.3 1.00
1.5 in 10 1.04
1 in 10 1.28
1 in 20 1.65
1 in 40 1.96
1 in 44 2.00
1 in 100 2.33
1 in 200 2.58
1 in 741 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 fcr at least 1200 psi (84.4 kgf/cm2) greater
than fl. 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-la), (4-lb), and (4-1c) can be used to calculate
a less conservative fCr.
4.2-Criteria for strength requirements
The amount by which the average strength of
a concrete mix fcr should exceed fC’ depends on
the criteria used in the specifications for a par-
ticular project. The following are examples of
calculations that would have to be made to select
STRENGTH TEST EVALUATION 9

10. the design strengths of a mix that will meet the
requirements of a particular code or specification.
4.2.1 Criterion No. 1-A stated maximum pro-
portion of random individual strength tests that
will be permitted to fall below fc’ 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 f:.
As an example, consider the situation where no
more than 1 in 10 random individual strengths
will be permitted to be below an f: of 4000 psi
(281 kgf/cmz).
Standard deviation method
Consider very good quality control as indi-
cated by a standard deviation of 450 psi (31.7
kgf/cm2). Using Eq. (4-la) and Table 4.1, we have
fCT = fc’+ to
= 4000 + 1.28 x 450
= 4580 psi (322 kgf/cm2)
As a result, for a structural design strength fJ
of 4000 psi (281 kgf/cm2), the concrete mixture
should be proportioned for an average strength of
not less than 4580 psi (322 kgf/cm2). 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-l) and Table 4.1, we have
fcr =
fcr =
--
--
Using this
fc
1 - 1.28 (0.10)
1.15 fi [see also Fig. 4.1 (a)]
4600 psi (324 kgf/cm2)
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 fJ.
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 fc’ 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 fc’ of 4000 psi (281 kgf /cm2).
Standard deviation method
Consider a standard deviation of 750 psi (53
kgf/cm2). Using Eq. (4-1c) and Table 4.1, we have
fCT = jc’+ $=
’ n 2.33(750)
= 4000 psi +
VT
= 5000 psi (351 kgf/cm2)
As a result, for a structural design strength fJ
of 4000 psi (281 kgf/cm2), the concrete mixture
should be proportioned for an average strength of
not less than 5000 psi (351 kgf/cm2).
Coefficient of variation method
Considering a coefficient of variation of 15 per-
cent and using Eq. (4-lb) and Table 4.1, we have
f
fc’CT =
1
tv--
v’
4000--
2.33 (0.15)
l- -
v3
= 5000 psi (351 kgf/cm2)
Using this approach the concrete
should be proportioned for an average
of not less than 5000 psi (351 kgf/cm2).
mixture
strength
4.2.3 Criterion No. 3-A certain probability that
a random individual strength test will be more
than a certain amount below f:.
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/cm2)
below fi 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 fi of 4000 psi (281
kgf/cm2) .
Standard deviation method
Considering a standard deviation of 750 psi
(53 kgf/cm2) and using Eq. (4-la) and Table 4.1,
we have
fc?_ = fc’- 500 + to
= 4000 - 500 + 2.33 (750)
= 5245 psi (369 kgf/cm2)
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-l) and Table 4.1, and a coefficient
of variation of 15 percent, we have
fcr = *; -;y-
4000 - 500
jcr = 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).
10 ACI STANDARD

11. TABLE 4.3-EVALUATION OF CONSECUTIVE LOW STRENGTH
TEST RESULTS
1
Number of
consecutive
tests
averaged
2 5
Averages less than indicated
Probability of
averages less
require investigation* than f,‘,t
percent
Criteria for original selection of for
1 test in 10
below fc
1 test in 100
less than
[fc’ - 500 psi
(35.2 kgf/cms]
I I I
For V = 15,
percent For given CT For given 0
fc’ - 500 + 0.76
fc’ - 500 + 0.88
fc’ - 500 + 1.14a
fc’ - 500 + 1.30
fc’ - 500 + 1.41
fr’ - 500 + 1.49
1 test in 10
below f0
10.0
3.5
E
0:2
0.1
*The probability of averages less than the levels indicated is approximately 2 percent if the
population average equals fGo and the standard deviation or coefficient of variation is at the
level assumed.
tIf the population average equals f CP 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 fc’.
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).
Standard deviation method
Using Eq. (4-la) and Table 4.1 and a standard
deviation of 750 (53 kgf/cm2), we have
fcr = 0.85 fc’ + to
= 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/cm2).
Coefficient of variation method
Using Eq. (4-l) and Table 4.1 and a coefficient
of variation of 15 percent, we have
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 fcr. 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 fcr or that (r 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.
0.85 fc’
fcr = ~1 - 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/cm2).
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
Column 5 shows the probability that the average
of any given number of consecutive tests will fail
to equal or exceed f: if the concrete is propor-
tioned to produce an average strength equal to
fcr. It can be seen that increasing the number of
tests to be averaged increases the likelihood that
fc’ 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 fG’. 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:. It should, however, be remem-
STRENGTH TEST EVALUATION 11

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 fcr.
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 ASTM 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
concrete control are illustrated in Fig. 4.4.
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-la) 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.
I 1 I I
’ ’ ’ ’ ’ ’ Charts for individual strength tests
I 1 ’ 1 1 1 ’
4 0 0 0 2 8 0
2000-- Required strength = fl+ tcr - - 1 4 0 ,
p- E
Moving average for strength c
Each point, average strength
W-
4000 Required average strength, fcr-,
of five previous test groups __280 z
3 0 0 - -
e,
E
- - - - - - - -
g lOO--
Averoge range for two cylinders = .0564 fcrA Each point average of _,
Average range tor three cylinders = 0846 fcr
I I II ! I I I I I I I I I I
ten previous ranges
11 1 11 11 1
0 4 8 I2 I6 20 24 28 32 36 4 0 4 4 48
Sample numbers
Fig. 4.4-Quality control charts for concrete.
12

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 any one 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 specimens
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. It 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 Em is the average range in Control Chart
(c) of Fig. 4.4. The within-test coefficient of
variation VI should not be greater than 5 percent
STRENGTH TEST EVALUATION
for
the
for
for
good control (Table 3.5), and the estimate of
corresponding average range will be:
Rm = (0.05 x l.l28)f,, = 0.05640&
groups of two companion cylinders
R, = (0.05 x 1.693)&r = O.O8465f,
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 if 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. If 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. If
possible, the correlation should be established by
laboratory tests before construction starts. If mix-
ing plants are located in one place for long enough
periods, it 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.
13

14. 4.6-Rejection of doubtful specimens
The practice of arbitrary rejection of test cylin-
It occasionally happens that the strength of one
ders which appear
cylinder from a group made from a sample devi-
“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.
a test of three or more specimens be discarded if
its deviation from a test mean is greater than
A test (average of all specimens of a sample)
30, and should be accepted with suspicion if its
deviation is greater than 20. If questionable varia-
should never be rejected unless the specimens are
tions have been observed during fabrication, cur-
the best
ing, or testing of a specimen, the specimen should
be rejected. The test average should be computed
from the remaining specimens.
ates so far from the mean as to be highly im-
probable. It is recommended that a specimen from
known to be faulty, since it represents
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, pp. l-4
to l-6.
2. Realism in the Application of ACI 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. Riisch, 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.
ACI STANDARD