Civil Engineering Reference
In-Depth Information
Table 9-10. Modification Factor for Standard
Deviation When Less Than 30 Tests Are Available
are insufficient or not available, the mixture should be
proportioned by the trial-mixture method. The approved
mixture must have a compressive strength that meets or
exceeds Â. Three trial mixtures using three different
water to cementing materials ratios or cementing mate-
rials contents should be tested. A water to cementing
materials ratio to strength curve (similar to Fig. 9-2) can
then be plotted and the proportions interpolated from the
data. It is also good practice to test the properties of the
newly proportioned mixture in a trial batch.
ACI 214
provides statistical analysis methods for
monitoring the strength of the concrete in the field to
ensure that the mix properly meets or exceeds the design
strength, ˘.
Modification factor for
Number of tests*
standard deviation**
Less than 15
Use Table 9-11
15
1.16
20
1.08
25
1.03
30 or more
1.00
* Interpolate for intermediate numbers of tests.
** Modified standard deviation to be used to determine required
average strength,
f
cr
.
Adapted from
ACI 318
.
Proportioning by Trial Mixtures
obtained by multiplying the standard deviation (
S
) for the
15 to 29 tests and a modification factor from Table 9-10.
The data must represent 45 or more days of tests.
The standard or modified deviation is then used in
Equations 9-1 to 9-3. The average compressive strength
from the test record must equal or exceed the
ACI 318
required average compressive strength, Â, in order for
the concrete proportions to be acceptable. The  for the
selected mixture proportions is equal to the larger of
Equations 9-1 and 9-2 (for ù
When field test records are not available or are insufficient
for proportioning by field experience methods, the con-
crete proportions selected should be based on trial mix-
tures. The trial mixtures should use the same materials
proposed for the work. Three mixtures with three different
water-cementing materials ratios or cementing materials
contents should be made to produce a range of strengths
that encompass Â. The trial mixtures should have a slump
and air content within ±20 mm (±0.75 in.) and ± 0.5%,
respectively, of the maximum permitted. Three cylinders
for each water-cementing materials ratio should be made
and cured according to ASTM C 192 (AASHTO T 126). At
28 days, or the designated test age, the compressive
35 MPa [5000 psi]) or
Equations 9-1 and 9-3 (for ù > 35 MPa [5000 psi]).
 = ˘ + 1.34
S
Eq. 9-1
 = ˘ + 2.33
S
- 3.45 (MPa) Eq. 9-2
 = ˘ + 2.33
S
- 500 (psi) Eq. 9-2
 = 0.90 ù + 2.33
S
Eq. 9-3
where
 = required average compressive strength of concrete
used as the basis for selection of concrete propor-
tions, MPa (psi)
˘ = specified compressive strength of concrete, MPa
(psi)
S
= standard deviation, MPa (psi)
When field strength test records do not meet the pre-
viously discussed requirements, Â can be obtained from
Table 9-11. A field strength record, several strength test
records, or tests from trial mixtures must be used for doc-
umentation showing that the average strength of the mix-
ture is equal to or greater than Â.
If less than 30, but not less than 10 tests are available,
the tests may be used for average strength documentation
if the time period is not less than 45 days. Mixture pro-
portions may also be established by interpolating between
two or more test records if each meets the above and
project requirements. If a significant difference exists
between the mixtures that are used in the interpolation, a
trial mixture should be considered to check strength gain.
If the test records meet the above requirements and limi-
tations of
ACI 318
, the proportions for the mixture may
then be considered acceptable for the proposed work.
If the average strength of the mixtures with the statis-
tical data is less than Â, or statistical data or test records
Table 9-11 (Metric). Required Average Compressive
Strength When Data Are Not Available to Establish a
Standard Deviation
Required average
Specified compressive
compressive strength,
strength,
f
c
, MPa
f
cr
, MPa
f
c
+ 7.0
Less than 21
f
c
+ 8.5
21 to 35
1.10
f'
c
+ 5.0
Over 35
Adapted from
ACI 318
.
Table 9-11 (Inch-Pound Units). Required Average
Compressive Strength When Data Are Not Available
to Establish a Standard Deviation
Required average
Specified compressive
compressive strength,
strength,
f
c
, psi
f
cr
, psi
f
c
+ 1000
Less than 3000
f
c
+ 1200
3000 to 5000
1.10
f
c
+ 700
Over 5000
Adapted from
ACI 318
.
