Handout On Concrete Mix Design
Handout On Concrete Mix Design
Handout On Concrete Mix Design
) written by
Mindess et al., Copyright: Pearson Education, Inc.
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Proportioning Concrete
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Mixes
constitutes “fair use”, that user may be liable for copyright infringement.
These materials are made available for the educational purposes of students
enrolled at the University at Buffalo. No further reproduction, transmission,
or electronic distribution of this material is permitted. The proportioning of concrete mixtures, more commonly referred to as mix design, is a
process that consists of two interrelated steps: (1) selection of the suitable ingredients
(cement, aggregate, water, and admixtures) of concrete and (2) determining their rela-
tive quantities ("proportioning") to produce, as economically as possible, concrete of
the appropriate workability, strength, and durability. These"proportions will depend on
the particular ingredients used, which will themselves depend on the application.
Other criteria, such as designing to minimize shrinkage and creep or for special chemi-
cal environments, may also be considered. However, although a considerable amount
of work has been done on the theoretical aspects of mix design, it still remains largely
an empirical procedure. And, although many concrete properties are important, most
design procedures are based primarily on achieving a specified compressive strength at
some given workability and age; it is assumed that if this is done, the other properties
(except perhaps resistance to freezing and thawing or other durability problems, such
as resistance to chemical attack) will also be satisfactory. But before turning to the mix
design methods now in common use, it is worthwhile to examine the basic design con-
siderations themselves in more detail.
221
222 Chapter 10 Proportioning Concrete Mixes Section 10.2 Fundamentals of Mix Design 223
design methods depend heavily on these two considerations. Bulletin 22, Research Laboratories of the Portland Cement Association (1948).
224 Chapter 10 Proportioning Concrete Mixes Section 10.2 Fundamentals of Mix Design 225
Coarse (37.5 within the band shown in Figure 10.3 are expected to produce cohesive concrete that
Fine to4.75 mm)
100 can be readily consolidated by high-frequency vibration and that will generally exhibit
100
80
90
Oil
s::: 80
·;;: 60
"'p,. w
"' Oil
70
i5
Q) .s 60
u ~
.... 40
~
Q)
"'
p,.
50
i5
Q)
u
....
Q)
40
20 ~
30
20
10
Aggregate size (mm) 0
0.15 0.3 0.6 1.18 2.36 9.5 19.5 37.5
FIGURE 10.1
Aggregate size (mm)
Grading curves indicating the specified grading limits (ASTM C 33) for fine aggregate and one size
of coarse aggregate. A combined grading curve (40% fine aggregate and 60% coarse aggregate for FIGURE 10.2
the midrange of the ASTM limits) and the corresponding Fuller-Thompson "ideal" grading curve
are also shown. Combined aggregate gradations, including designations of size fractions as particles that
aid workability (W) , intermediate particles (/), and quality filler (Q) . (Adapted from J.M.
Shilstone, Sr.)
poor workability. In addition, very fine particles cannot form densely packed aggre-
gates; packing density decreases as the average particle size decreases. To improve con- 45
crete behavior, ASTM C 33 (and CSA A23.1) requires that 2 to 10% of the fine
Q)
aggregate must pass the 150-µ,m (No.100) sieve, and 10 to 30% must pass the 300-µ,m >
Q)
·;;:
(No. 50) sieve. In terms of packing, the gradations used in ASTM C 33 can only ,...., 40
00
approximate the Fuller curve, as shown in Figure 10.1. .... ci
Shilstone3 has developed an empirical procedure that uses a combined aggre- oZ ........
g9 35
~
gate gradation to optimize concrete workability, economy, and strength. As shown in ;E? ~[_...;-.- i..--
Figure 10.2, the combined aggregate is characterized as consisting of material equal to :s~ L---[_...;-.-
and larger than 9.5mm (3/sin.) (designated as Q for quality filler), material smaller
..0 .
"'N
.!<I Oil
.... s::: 30
~
L--- ~
o·~ ~ · ~
than 9.5 mm (3/s in.) and retained on the 2.36-mm (No. 8) sieve (designated as I for ~ p,.
~ __.. L---' L---'
intermediate particles that fill major voids and aids in mix "mobility"), and material i5
Q)
25
i .... L..--
smaller than 2.36-mm (designated as W for particles that aid workability). Shilstone u
....
Q)
observed that experimentally "optimum" combined aggregate gradations can be ex- e:...
pressed by the relationship between a workability factor [the fraction of total aggre- 20
gate passing the 2.36-mm (No. 8) sieve = Wl(Q + I + W)] and a coarseness factor 70 60 50 40 30 20 10 0
100 90 80
[ratio between the weight fraction of particles retained on the 9.5-mm (3/s-in.) sieve to
Coarseness factor
the weight of all particles retained on the 2.36-mm (No. 8) sieve = Q/(Q + I)] . Mixes (Percent of plus 2.36 mm (No. 8) retained on 9.5-mm (3/8 in.) sieve]
FIGURE 10.3
3J.
M. Shilstone, Sr., "Concrete Mixture Optimization," Concrete International, Vol. 12, No. 6, pp. 33-39 (June Band of aggregate gradations on coarseness factor chart that produce optimum concrete mixtures.
1990). (Adapted from J.M. Shilstone, Sr.)
226 Chapter 10 Proportioning Concrete Mixes . Section 10.3 ACI Method of Mix Design 227
the lowest water demand for a given cement content. The concrete used to develop Mix Design Procedures
Figure 10.3 contained 335 kg/m 3 ( 564 lb/yd 3 ) of cement. Since cement particles also aid 1. Required information. Before starting the mix design process, information is required
workability, the W factor should be adjusted by treating any increase or decrease from on both the materials to be used and the structure into.which the concrete will be placed.
this cement content as an increase or decrease in the W content of the combined ag- Raw material properties include sieve analyses of both the fine and coarse aggregates,
gregate (accounting for differences in the specific gravities of the fine aggregate and unit weight of the coarse aggregate, bulk specific gravities, and absorption capacities of
cement). the aggregates. Information on the structure includes the type and dimensions of the
The grading limits for fine and coarse aggregate shown in Figure 10.1 are, like structural members, the minimum space between reinforcing bars, the require~
the combined gradations in Figures 10.2 and 10.3, based on practical experience strength, and the exposure conditions to which the concrete will be su~efed.
rather than on theory. In fact, it is possible to make a satisfactory concrete from al-
most any type of aggregate grading, although gradations outside the limits of Figure 2. Choice of slump. Usually, slump will be specified for a particular job, to take into
10.1 (and even some gradations within these limits) may be uneconomical and diffi- account the anticipated methods of handling and placing the concrete. However, where
cult to handle with regard to segregation, consolidation, and finishing. The procedures the slump has not been specified, appropriate values can be chosen from Table 10.1,
developed by Shilstone are fairly new and are not, as yet, standard practice in the con- which applies when the concrete is to be consolidated by vibration. As a general rule,
crete industry. the lowest slump that will permit adequate placement should be selected. This, howev-
er, does not mean that the minimum slump should automatically be chosen from Table
10.1. "Adequate placement" requires the consideration of job-site conditions, which
often leads fO me seiectio-;: of.a slump cfoser-tothe maximum recommenaecrvalue-:-ms
10.3 ACI METHOD OF MIX DESIGN
beoomingi~singlycommon to design a concrete for a kiwer.sfiimp-aiid thell'"ii;rease
There are a number of different methods of mix design available. Although they are it to a higher value using a water-reducing admixture.
not directly comparable, they do give approximately the same relative proportions of 3. Maximum aggregate size. Generally, the largest maximum size of aggregate avail-
materials, and all are capable of yielding suitable concrete mixes. The most common able (and consistent with the limitations to be listed) should be used, as this will mini-
method used in North America is that established by ACI Standard Practice 211.1, and mize the required cement content. The limitations on maximum aggregate size (see
this method will be described here in some detail. It must be remembered, however, Section 7.1) are as follows:
that any mix design method will provide only a first approximation of proportions.
These must be checked by trial batches in the laboratory or in the field and then ad- a. For reinforced (or prestressed) concrete, the maximum size may not exceed one-
justed as necessary to produce the desired concrete characteristics. With any given set fifth of the minimum dimension between forms, or three-fourths of the minimum
of materials, it may be found that considerable deviations from the ACI recommended
practice may be necessary. Once sufficient experience with local materials is acquired, TABLE 10.1 Recommended Slumps for Various Types of Construction. a,b
the tables used in the ACI method should be modified to take their properties into
Slump (mm) Slump (in.)
account. Types of Construction Max. < Min. Max.< Min.
As was stated earlier, the job specifications may dictate certain mix require-
ments, such as minimum cement contents and w!c ratios, slump, air content, maximum Reinforced foundation walls 75 25 3 1
and footings
aggregate size, strength, the use of admixtures, or other special requirements. But re- Plain footings, caissons, and 75 25 3
gardless of the specification requirements, the establishment of the batch weights substructure walls
[note that it is nearly always preferable to batch concrete by weight (Chapter 11) Beams and reinforced walls 100 25 4 1
rather than by volume] can best be accomplished by following the sequence of steps Building columns 100 25 4 1
laid out next. This will ensure that the characteristics of the available materials are Pavements and slabs 75 25 3 1
Mass concrete 50 25 2
properly considered in combining them into a suitable concrete mixture. In summary,
the mix design process consists of (1) determining the job parameters-aggregate "From ACI 211.1. Reproduced with permission.
b Slump may be increased when chemical admixtures are used, provided that the ad-
properties, maximum aggregate size, slump, w/c ratio, and admixtures; (2) calculating mixture-treated concrete has the same or lower water-cement ratio or water--cemen-
the batch weights; and (3) adjusting to the batch weights based on a trial mix made titious material ratio and does not exhibit segregation potential or excessive bleeding.
according to these calculations. <May be increased 25 mm (1 in.) for methods of consolidation other than vibration.
Section 10.3 ACI Method of M ix Design 229
228 Chapter 10 Proportioning Concrete Mixes
clear spacing between bars, strands, bundles of bars, or between the steel and the TABLE 10.2 Approximate Mixing Water and Air Content Requirements for Different Slumps and Nominal
formwork. 4 Maximum Sizes of Aggregates. a,b
b. For slabs, the maximum size may not exceed one-third the slab depth. Water, kg/m 3 (lb!yd 3 ) of Concrete for Indicated Nominal Maximum Sizes ofA ggregate
If it is shown by experience that it is possible to place the concrete without honey- Slump 9.5 (318 12.5 (112 19 (314 25 (1 37.5 (2' 75' (3'
combing or voids, these requirements may be relaxed. It has also been found that, at a mm in. mm in.) mm in.) mm in.) mm in.) mm in. ) mm in.)
given w!c ratio, higher compressive strengths can be achieved with smaller maximum
sizes of aggregates. There is, thus, a trend toward the use of reduced maximum aggre- Non-Air-Entrained Concrete
gate sizes, especially for high-strength concretes (see Chapter 19). In many areas, the 30-50 1-2 210 (350) 200 (335) 185 (315) 180 (300) 160 (275) 155 (260) 130 (220)
largest sizes available are 19 or 25 mm(% in. or 1 in.). It should also be remembered 80-100 3-4 225 (385) 215 (365) 200 (340) 195 (325) 175 (300) 170 (285) 145 (245)
that, for a given job, it may be unwise to recommend different maximum aggregate 150-180 6-1 240 (410) 230 (385) 210 (360) 205 (340) 185 (315) 180 (300) 160 (270)
Approximate amount
sizes for different parts of the structure, as this may lead to confusion and increases the of air in non-air-
probability of error. entrained concrete, % 3 2.5 2 1.5 1 0.5 0.3
4. Estimation of mixing water and air content. As we have seen in Chapter 9, t~~ork Air-Entrained Concrete
~bjlity of concrete is dependent primarily on the paste content of the concrete; the 30-50 1-2 180 (305) 175 (295) 165 (280) 160 (270) 145 (250) 140 (240) 120 (205)
amount of entrained air; and the maximum size, grading, and particle shape of the aggre- 80-100 3-4 200 (340) 190 (325) 180 (305) 175 (295) 160 (275) 155 (265) 135 (225)
gate. An estimate of the water requirement to produce different slumps for both 150-180 6-7 215 (365) 205 (345) 190 (325) 185 (310) 170 (290) 165 (280) 155 (260)
Recommended average
air-entrained and non-air-entrained concrete can be obtained from Table 10.2, which is total air content, % , for
based on experience obtained over many years C?f practice. It is, however, better to estab- level of exposure:
lish these numbers from experience with the actual materials in question rather than Mild exposure 4.5 4.0 3.5 3.0 2.5 2.0 l.5d
resorting to the use of Table 10.2. When water-reducing admixtures are used, these val- Moderate exposure 6.0 5.5 5.0 4.5 4.5 4.0 3.5d
ues should be decreased according to the amount of water reduction anticipated. Table Severe exposure' 7.5 7.0 6.0 6.0 - 5.5 5.0 4.5 d
10.2 also shows the approximate amount of entrapped air to be expected in non-air- a Adapted from ACI 211.1. Reproduced with permission.
entrained concrete and gives the recommended levels of air entrainment (when bThese quantities of mixing water are for use in computing cement factors for trial batches. They are maxima for rea-
sonably well-shaped, angular, coarse aggregates graded within limits of accepted specifications.
required) for different maximum sizes of aggregate and for three different levels of
' The slump values for concrete containing aggregate larger than 37.5 mm (1 1/2 in.) are based on slump tests made
severity of exposure. Since there is frequent pressure from the job site for concrete with
after removal of particles larger than 37.5 mm (1 1/z in.) by wet screening.
"more slump" (which is often obtained by adding more water rather than by adding dFor concrete containing large aggregates, which will be wet screened over the 37.5-mm (1 1/z-in.) sieve prior to testing
more paste, leading to a higher w/c ratio and lower strength), it is suggested that the trial %
for air content, the percentage of air expected in the 37.5 mm (1 in.) minus material should be as tabulated in the
batches of the mix used to develop the strength relationships be made to represent the 37.5-mm (1 1/z -in.) column. However, initial proportioning calculations should include the air content as a percent of
most unfavorable combination of air content and water content. That is, both the max- the whole.
imum allowable air content and the maximum allowable slump should be used in these ' These values are based on the criterion that 9% air is needed in the mortar phase of the concrete. If the mortar vol-
batches rather than using average values. This will help prevent overestimating the ume will be substantially different from that determined in this recommended practice, it may be desirable to calcu-
late the needed air content by taking 9% of the actual mortar volume.
strength.
with a pozzolan.5 Of course, it is possible that the specifications may be based on
5. Water/cement or water/cementitious material ratio. The selection of the appropri-
a required strength at a time other than 28 days (e.g., at the time when forms are
ate w/c or w/cm ratio may be governed not only by strength, but also by durability
to be stripped), or the design may require the use of another standard type of
requirements: portland cement (Types II, III, IV, or V), blast furnace slag, or very high quanti-
a. Strength. In the absence of strength vs. w/c ratio data for the specific materials, a ties of pozzolans. In these cases, Table 10.3 is not applicable. The designer must
conservative estimate can be made for the expected 28-day compressive strength develop his or her own data for these cases, or when the design is governed by a
from Table 10.3, when Type I portland cement is used, either alone or together flexural strength requirement. It is always more desirable to develop the appro-
priate strength-time-w/cm ratio relationships for the materials that are actually
to be used on the job. In this way, the effects of admixtures can also be determined.
4ACI 211.1 and ACI 318 (Building Code Requirements) do not impose the limitation based on the spacing
5Although ACI 211.1 does not specifically address the use of blast furnace slag, the procedures described
between steel and formwork. This oversight can result in voids and honeycombing as larger aggregate parti-
here can be applied equally well for all mineral admixtures.
cles become wedged between the reinforcing steel and the face of the form.
230 Chapter 10 Proportioning Concrete Mixes Section 10.3 ACI Method of Mix Design 231
TABLE 10.3 Relationships between Water/Cement or Water/Cementitious Materials Ratio TABLE 10.4 Maximum Permissible Water/Cement or Water/Cementitious Material Ratios for Concrete in
and Compressive Strength of Concrete. " Severe Exposures.a,b
to reach the design w/c ratio, consistent with any specified limitations on cement Step 4: Estimation of mixing water and air content. Since the concrete will be ex-
content. If the water content must be increased to obtain the desired slump, then posed to freezing and thawing, it must be air entrained. From Table 10.2,
the w/c ratio will also be increased. In this case, additional cement must be added the air content recommended for severe exposure is 6.0%; the water re-
until the design w/c ratio is again achieved (or the entire mix redesigned). quirement is 180 kg/m3 (305 lb/yd 3 ).
b. If the desired amount of entrained air is not achieved, the amount of air-entraining Step 5: Water/cement ratio. From Table 10.3, the (conservative) estimate of the
admixture should be reestimated. The mixing water required should then be in- required w/c ratio to give a 28-day compressive strength of 30 MPa (4500
creased or decreased by 3 kg/m3 (5 lb/yd3 ) for each decrease or increase of 1 % air psi) is 0.45. This does not exceed the limits based on durability in Table 10.4
entrainment, because of the influence of entrained air on workability. (or Table 10.5).
c. If the weight method of proportioning is used and if the estimated weight of fresh
Step 6: Calculation of cement content. The required cement content, based on the
concrete is incorrect, this can be reestimated from the unit weight of the trial
results of Steps 4 and 5, is 180/0.45 = 400 kg/m3 (305/0.45 = 678 lb/yd3 ) . 10
batch, making allowance for the necessary changes in air content.
d. Any adjustment will change the yield, and therefore new batch weights must then Ste_p 7: Estimation of coarse aggregate content. Interpolating in Table 10.8 for the
be calculated, following the foregoing procedure from Step 5 on. fineness modulus of the fine aggregate of 2.70, the volume of dry-rodded
coarse aggregate per unit volume of concrete is 0.63. Therefore, the
coarse aggregate will occupy 0.63 m3/m3 (or 0.63 x 27 = 17.01 ft 3/yd3 ).
Example Mix Design The OD weight of the coarse aggregate is 0.63 x 1600 = 1008 kg
To illustrate the mix design procedure, consider the following sample problem: Concrete (17.01 X 100 = 1701lb ). The SSD weight is 1008 x 1.01 = 1018 kg
is required for an exterior column to be located above ground level in an area where it (1701 x 1.01 = 1718 lb). •
will be wet and subjected to substantial freezing and thawing. The concrete is required to Step 8: Estimation of fine aggregate content. The fine aggregate content can be
have an average 28-day compressive strength of. 30 MPa (about 4000 lb/in. 2 ). 9 For the established either by the mass (weight) method or by the absolute volume
conditions of placement, the slump should be between 75 and 100 mm (3 and 4 in.). The method.
column is 635 mm (25 in.) square with a minimum clear space for aggregate of 50 mm (2 a. Mass (weight) method. From Table 10.9, the estimated concrete weight
in.). The properties of the materials are as follows: is 2280 kg/m3 (3840 lb/yd3 ). Although for a first trial it is not generally
Cement: Type I, specific gravity = 3.15 necessary to use the more exact calculation based on Eq. (10.6), this
value will be used here:
Fine aggregate: Bulkspecificgravity (SSD) = 2.63; absorption capacity = 1.3%;
surface moisture = 4.2% based on SSD state; fineness modulus = 2.70 um= (10) (2.66) (100 - 6) + 400(1 - 2.66/3.15) - 180(2.66 - 1)
Coarse aggregate: Maximum size = 19 mm(% in.); bulk specific gravity (SSD) = 2264kg/m3
= 2.68; absorption capacity = 1.0%; surface moisture = 0.5% based on SSD
state; dry-rodded unit weight = 1600 kg/m3 (100 lb/ft3 ) Using Eq. (10.7), the equivalent value of 3812 lb/yd3 is obtained. The
weights already determined are water = 180 kg (305 lb), cement =
The sieve analyses of the coarse and fine aggregates fall within the limits specified in 400kg(678lb), and coarse aggregate (SSD) = 1018kg (1718lb).
ASTM C 33. With this information, the mix design will now be carried through in de- Therefore, the weight of the fine aggregate (SSD) is 2264 - 180 -
tail, using the sequence of steps outlined. 400 - 1018 = 666kg (3812 - 305 - 678 - 1718 = l llllb).
b. Volume method. Knowing the weights and specific gravities of water, Step 10: Trial batch. A trial batch is now made using the proportions calculated.
cement, and coarse aggregate and knowing the air volume, we can cal- The properties of the concrete in the trial batch (including unit weight)
culate the volumes per m3 (yd 3 ) occupied by the different ingredients: must be compared with the desired properties, and the mix design must
Water: 180/1000 (305/62.4) 0.180 m3 ( 4.89 ft3)
be corrected as described. To illustrate this process, consider the follow-
Cement: 400/(1000 x 3.15) [678/62.4 x 3.15] 0.127 m3 (3.45 ft 3 ) ing trial batch results:
Coarse Aggregate (SSD) 11 :1018/(1000 x 2.68) 0.380 m3 Small trial batches are prepared based on the example m 3 and yd 3 mix designs
[1718/(62.4 x 2.68)] (10.27 ft 3 ) (0.015 m 3 and 0.02 yd 3, respectively). The desired slump is 100 mm (4 in.), and the de-
Air: 0.06 (0.06 X 27) 0.060m3 (1.62 ft 3 ) sired air content is 6%. During the course of the trial match, we find that extra water is
Total 0.747m 3 (20.23 ft 3 ) needed to achieve the desired slump. The final properties of the concrete are
slump = 75 mm (3 in.), air content = 5%, and unit weight = 2286 kg/m3 (142.6 lb/ft3 ).
Therefore, the fine aggregate must occupy a volume of
The weights used in the trial batches are expressed in terms of SSD aggregate:
1 - 0.747 = 0.253 m 3 (27 - 20.23 = 6.77 ft 3 ) . The required SSD
weight of the fine aggregate = 0.253 X 2.63 X 1000 = 665 kg
Cement: 6.00kg (13.56 lb)
( 6.77 x 2.63 x 62.4 = lllllb ). As may be seen, this is essentially
Coarse aggregate (SSD): 15.27 kg (34.36 lb)
the same as the weight calculated according to the weight method.
Fine aggregate (SSD): 9.98 kg (22.22 lb)
Step 9: Adjustment for moisture in the aggregate. Since the aggregates will be nei-
Water (includes surface
ther SSD nor OD in the field, it is necessary to adjust the aggregate weights
moisture on wet
for the amount of water contained in the aggregate. (Note that very dry ag-
aggregate): 2.84 kg (6.40 lb )
gregates will absorb water from the mix, and this too must be allowed for.)
Total batch weight: 34.09 kg (76.54 lb)
Only surface water need be considered; absorbed water does not become
part of the mix water. For the given moisture contents, the adjusted aggre-
Based on manufacturers recommendations, air-entraining agent was added at a rate of
gate weights become (see Section 7.1):
0.23 L/m3 (6 fluid ounces/yd3 ). •
Coarse aggregate (wet) = 1018 (1.005) = 1023kg/m3 The batch weights and unit weight can now be used to determine the actual quan-
[1718 (1.005) = 1727 lb/yd 3] tities used on a m 3 (yd3 ) basis:
Fine aggregate (wet) =665(1.042) =693kg/m3
[1111 (1.042) = 1158 lb/yd 3] _ 2286 kg/m3 _ 3
Batch factor - 34 _09 kg/batch - 67.06 batches/m
Surface moisture contributed by the coarse aggregate is 0.5%; by the fine
- [ 142.6 lb/ft3x 27 ft 3/yd3-
aggregate 4.2%. The mixing water (that needs to be batched separately)
is then
3]
- 7654 lb/batch - 50.30 batches/yd
180 - 1018(0.005) - 665(0.042) = 147kg/m3
m3 batch yd 3 batch
[305 - 1718(0.005) - 1111(0.042) = 250 lb/yd3] Cement: 6.00 x 67.06 = 402 kg (13.56 x 50.30 = 682 lb)
Coarse Aggregate (SSD): 15.27 x 67.06 = 1024 kg (34.36 x 50.30 = 1728 lb)
Thus, the estimated batch weights per m3 (yd3 ) are: Fine Aggregate (SSD) 9.98 x 67.06 = 669 kg (22.22 x 50.30 = 1118 lb)
Water (to be added) = 147 kg (250 lb) Water: 2.84 x 67.06 = 190 kg (6.40 x 50.30 = 322 lb)
Cement = 400 kg (678 lb)
Coarse aggregate (wet) = 1023 kg (1727 lb)
Fine aggregate (wet) = 693kg (1158lb) Note that, due to the extra water required and lower air content, the actual weights of
Total = 2263 kg (3813 lb) the ingredients differ from the original values.
The mix design must now be modified to obtain the desired slump, air content,
and w/c ratio.
The water content for a 100-mm (4-in.) slump will be 190 kg/m 3 + 6 kg/m3 [to
11 If bulk specific gravities of the aggregates are given on an OD basis, then the OD weight should be used to
increase the slump from 88 mm (3 in.)] - 3 kg/m 3 [to take into account the extra
calculate the solid volume of the coarse aggregate, and the weight of the fine aggregate will be determined
slump that will be obtained as the 5% actual air content is increased to the desired
on an OD basis also. 6%] = 193 kg/m 3 (322 + 10 - 5 = 327 lb/yd3 ).
240 Chapter 10 Proportioning Concrete Mixes Problems 241
We now proceed from Step 5 to recalculate the batch weights. Powers, T. C., The Properties of Fresh Concrete. John Wiley & Sons, Inc., New York (1968).
Step 5: w/c = 0.45 is unchanged Proportioning Concrete Mixes, SP-46. American Concrete Institute, Detroit, Ml (1974).
Shilstone, J.M., Sr., "Concrete Mixture Optimization," Concrete International, Vol. 12, No. 6,
Step 6: Cement content = 193/0.45 = 429 kg (327/0.45) = 727 lb
pp. 33-39 (June 1990).
Step 7: Coarse aggregate (SSD) content = 1018 kg (1718 lb) is unchanged Standard Practice for Selecting Proportions for Normal, Heavyweight, and M ass Concrete, ACI
Step 8: Fine aggregate (SSD) content: For this problem, we will use the "volume" 211.1. American Concrete Institute, Farmington Hills, MI (1991).
method.
10.10 The following batch weights (cubic meter, SSD basis), selected using ACI 211.1,
produced concrete with a unit weight of 2280 kg/m 3 , a slump of 75 mm, and an
air content of 5%.
Cement: 408 kg/m 3 (specific gravity 3.15).
Water: 163 kg/m3 .
Coarse aggregate: 1018 kg/m3 [19 mm, bulk specific gravity (SSD) = 2.62, ab-
sorption capacity = 3.8%, dry-rodded unit
weight = 1505 kg/m3].
Fine aggregate: 653 kg/m3 [bulk specific gravity (SSD) = 2.58, absorption
capacity = 1.0% , fineness modulus = 2.50].
Air-entraining agent: 0.30 L/m3 .
a. What volume of concrete was produced?
b. What were the actual mix proportions on a cubic meter basis?
c. What batch quantities (cubic meter, SSD basis) should be used to produce
concrete with a 100-mm slump and 61/z % air content?
10.11 The following batch weights (cubic yard, SSD basis), selected using ACI 211.1,
produced concrete with a unit weight of 141.8 lb/ft 3, a slump of 2 in., and an air
content of 4%.
Cement: 573 lb/yd3 (specific gravity 3.15).
Water : 275 lb/yd 3.
Coarse aggregate: 1657 lb/yd3 [% in., bulk specific gravity (SSD) = 2.58,
absorption capacity = 3.5%, dry-rodded
unit weight = 94 lb/ft3].
Fine aggregate: 1247 lb/yd3 [bulk specific gravity (SSD ) = 2.62, absorption
capacity = 1.5%, fineness modulus = 2.70].
Air-entraining agent: 8 fl. oz/yd3•
a. What volume of concrete was produced?
b. What were the actual mix proportions on a cubic yard basis?
c. What batch quantities (cubic yard, SSD basis) should be used to produce
concrete with a 4-in. slump and 61/2 % air content?