1. CON 124
Basic Concrete Mix Design Proportioning
Session 3
Examples of Concrete Proportioning

2. Examples of Proportioning
Concrete Mixtures
 Absolute volume method
 Trial mixture using the Water-Cement ratio
method

3. Proportioning Concrete Mixtures
Example 1
Using the Absolute Volume Method
Vol
Abs Vol Density = Weight/Volume
(no voids)
Specific Gravity =
Abs Vol Density / Density of Water

4. Proportioning Concrete Mixtures
Absolute Volume Method for Example 1 using
the equations below:
Abs Vol=Wt/(Specific Gravity x Density of Water)
Wt=Abs Vol x Specific Gravity x Density of Water
Density of Water = 62.4 lbs per cu ft ( @ 40C)
1 Cubic yard concrete = 27 cubic feet

5. Conditions for Example 1
 Concrete for a building foundation
 Specified Compressive Strength: f c= 3500 psi
 Type I cement; Relative Density = 3.15
 Design for minimum 3 in of concrete cover
 Minimum distance between reinforcement bars is 4 in;
 Only admixture allowed is air entrainment
 No statistical data on mixes available
 Coarse Aggregate: ¾ in gravel; OD Relative Density = 2.68;
Absorption = 0.5%; Oven dry density = 100 lbs/cuft; Moisture
= 2%
 Fine Aggregate: Natural sand; OD Relative Density = 2.64;
Absorption = 0.7%; Moisture = 6%; Fineness Modulus = 2.80

6. Specifications for Example 1
 Strength: No statistical data available; fcr = fc +
1200; therefore, fcr = 3500 + 1200 = 4700 psi (Table
11 CON 124 Proportioning Methods)
 Water to Cement ratio: No required Max (Table 1
CON Proportioning and Mix Design); Recommended
W/C ratio for fcr = 4700 psi , 0.42 interpolated (Fig 1
or Table 3 CON 124 Proportioning and Mix Design)

7. Specifications for Example 1 (Cont)
 Coarse Aggregate Size: ¾ in nominal maximum size
adequate ¾ distance between reinforcing bars also
between reinforcing bars and forms (cover)
 Air Content: Target air of 6% needed to improve
workability and reduced bleeding. Design 6% +/- 1%,
Max of 7%
 Slump: Not specified, range 1 to 3 in adequate
(foundations, CON 124 Proportioning and Mix
Design)

8. Specifications for Example 1 (cont)
 Water Content: 3-in slump, air entrained concrete,
¾ in nominal maximum size aggregate; requires 305
lbs/cu yd (Fig 3 and Table 5,CON 124 Proportioning
and Mix Design); Crushed gravel particles reduce
water by 35 lbs, Estimated water content of 270 lbs
 Cement Content: Based on max W/C ratio and water
content; 270 lbs/0.42 = 643 lbs

9. Specifications for Example 1 (cont)
 Coarse Aggregate Content: Bulk volume CA recommended
using a fine aggregate Fineness Modulus of 2.80 is 0.62 (Fig 3
or Table 4, CON Proportioning and Mix Design); CA (oven dry)
weighs 100 lbs/cu ft, thus for a cubic yard of concrete(27 cu ft)
requires 100x27x0.62 = 1674 lbs/cu yd
 Admixture Content: 7% air, 0.9 fl oz/100 lbs of cement
 Fine Aggregate Content: Volume is determined by subtracting
absolute volumes of known ingredients from 27 cu ft/ cu yd
(see next slide), Absolute Volume = 27.0 – 19.50 = 7.50 cu ft;
Weight of dry fine aggregate = 7.50x2.64x62.4 = 1236 lbs

10. Absolute Volume Computation for
Fine Aggregate Content
270
Water = = 4.33 ft3
1 • 62.4
643
Cement = 3.15 • 62.4 = 3.27 ft3
7.0 • 27
Air = = 1.89 ft3
100
Coarse 1674
aggregate = = 10.01 ft3
2.68 • 62.4
Subtotal = 19.50 ft3
Fine aggregate volume=27-19.50= 7.50 ft3
Fine aggregate mass =7.50 • 2.64 • 62.4 = 1236 lb

11. Mixture Design for Example
1 per Cubic Yard
 Water: 270 lbs
 Cement: 643 lbs
 Coarse Aggregate (dry): 1674 lbs
 Fine Aggregate (dry): 1236 lbs
 Total weight: 3823
 Air-entraining admixture: 5.8 fl oz
 Slump: 3-in (+/- ¾ in for trial batch)
 Air Content: 7%

12. Trial Batch Corrections for Moisture in
Aggregates
 Dry Batch Weights need correction for absorbed and
surface moisture (MC)
 Mixing water reduction due to amount of free
moisture contributed by aggregates
 Coarse Aggregate (CA) MC is 2%; Fine Aggregate (FA)
MC is 6%
 CA (2% MC) = 1674 lbs x 1.02 = 1707 lbs
 FA (6% MC) = 1236 lbs x 1.06 = 1310 lbs
 Estimated mix water: 270 lbs – (1674 x 0.015) –
(1236 x 0.053) = 179 lbs

13. Estimated Batch Weights for Aggregate
Moisture Content
 Water (to be added): 179 lbs
 Cement: 643 lbs
 CA (2% MC,wet) 1707 lbs
 FA (6% MC, wet) 1310 lbs
 Total Batch Weight: 3839 lbs/ 1 Cubic Yd

14. Laboratory Trial Batch
(2.0 cu ft; or 2/27 cu yd)
 Trial batch concrete needed for air, slump, and
casting of cylinders for strength
 Water: 179 lbs x 2/27 = 13.26 lb
 Cement: 643 lbs x 2/27 = 47.63 lb
 CA, wet: 1707 lbs x 2/27 = 126.44 lb
 FA, wet: 1310 lbs x 2/27 = 97.04 lb
 Total laboratory trial batch: 284.37 lbs
 Air Entraining admixture: 5.8 fl oz x 2/27 = 0.43

15. Laboratory Trial Batch Data
 Lab trial batch concrete testing:
 Measured Slump, 4-in
 Air Content, 8%
 Density (unit weight), 141.49 lbs
 Pre-measured water remained unused, original amount of
water was 13.26 lbs, only used 13.12 lbs
 Mixture Design: Water = 13.12 lbs, Cement = 47.63
lbs, CA (2% MC) = 126.44 lbs, FA (6%MC) = 97.04;
Total trial batch = 284.23 lbs/ 2.0 cu ft

16. Yield of Laboratory Trial Batch
 Total laboratory batch weight : 284.23 lbs
 Laboratory density (unit weight): 141.49
lbs/cu ft
 Yield: 284.23lbs/141.49 lbs/cu ft = 2.009 cu ft

17. Mixing Water Content of Trial Batch for
1- cubic yard
 Water added: 13.12 lbs
 Free Water CA: 126.44/1.02 x 0.015 = 1.86 lbs
 Free Water FA: 97.04 /10.6 x 0.053 = 4.85 lbs
 Total Water: 19.83 lbs
 Mix water needed / cu yd for same slump: 19.83 lbs
x 27.00 cu ft/cu yd/2.009 cu ft = 267 lbs

18. 1 yard Concrete Trial Batch
Adjustments
 Measured 4-in slump unacceptable more than 0.75 in above designed 3-
in max
 Trial yield slightly exceeds design
 Air content of 8% is unacceptable, more than 0.50% above designed 7%
max
 Reestimate amount of air entraining admixture for a 7% max air content,
and adjust water to obtain 3-in slump
 Increase mixing water by 5 lbs for each 1%;reduce mixing water by 10 lbs
for 1-in reduction in slump:
(5 x 1) – (10 x 1) + 267 lbs = 262 lbs/cu yd
 With less mixing water needed, less cement required for desired water-
cement ratio of 0.42:
262 lbs/cu yd/0.42 = 624 lbs/ cu yd

19. New Adjusted Concrete Batch Volumes
per Cubic Yard
 Water: 262/1 x 62.4 = 4.20 cu ft
 Cement: 624/3.15 x 62.4 = 3.17 cu ft
 CA: 1674/2.68 x 62.4 = 10.01 cu ft
 Air: 7.0/100 x 27.0 = 1.89 cu ft
 Total from above: 19.27 cu ft
 FA: 27.00 – 19.27 = 7.73 cu ft

20. Adjusted Dry Weights for 1 Cubic Yard
 FA (dry): 7.73 x 2.64 x 62.4 = 1273 lbs
 Air dosage; 0.8 fl oz/ 100 lbs of cement to achieve 7% air: 0.8 fl oz x
624/100 = 5.0 fl oz
 Designed Batch weights:
Water = 262 lbs
Cement = 624 lbs
CA (dry) = 1674 lbs
FA (dry) = 1273 lbs
Total Batch = 3833 lbs
Estimated Concrete Density (unit weight) at SSD
(262 + 624 + (1674 x 1.005) + (1273 x 1.007)) divided by 27 = 142.60 lb/cu ft

21. Example 2 Proportioning by Trial
Mixtures Using W/C ratio
Trial batching verifies
that a concrete mixture
meets design
requirements prior to
use in construction.

22. Example 2 Proportioning by Trial
Mixtures Using W/C ratio
 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.
 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 tested at 28 days.

23. Laboratory Trial Mixtures Using the
Water-Cement Ratio
 Conditions:
 Foundation wall requiring air-entrained concrete exposed to moderate
sulfate soils
 Compressive strength, fcr, 4000 psi @ 28 days, Type II cement
 Minimum thickness of wall is 10-in; concrete cover over ½-in diameter
reinforcing bars 3-in
 Specifications:
 Water-cement ratio vs compressive strength relationship based on
field and previous lab data
 Test records of materials used, std dev is 300 psi
 Max W/C ratio for the above conditions should be 0.50
(Table 1 CON 124 Concrete Proportioning and Mix Design)

24. Concrete Trial Mixture Designed
Compressive Strengths
 Standard Deviation (S) of 300 psi
 fcr = fc + 1.34S = 4000 + 1.34 (300) = 4402 psi
 Or fcr = fc + 2.33S – 500 = 4000 + 2.33 (300) – 500 =
4199 psi
 Therefore fcr = 4400 psi
 W/C ratio for air-entrained concrete is 0.55 for an fcr
of 4400psi; Exposure Conditions requirements
govern; Thus W/C ratio of 0.50 used producing
higher strengths than needed to satisfy structural
needs

25. Relationship between
strength and water to
cement ratio based on
field and laboratory data
for specific concrete
ingredients.

26. Example 2 Concrete Trial Batch
Mixture Data
 Aggregate: 1½-in max size is satisfactory; less than
1/5 wall thickness; less than ¾ the clear distance
between reinforcing bars, as well as forms
 Air Content: Exposure conditions and workability
require moderate level, target concrete air with an
1½-in aggregate is 4.5%+/- 1%, aim for 5.5%+/- 0.5%
in trial batch
 Slump: 1-3-in for placing a reinforced concrete
foundation wall; trial batch for 3-in +/- 0.75 in

27. Relationship
between:
 Slump
 Agg. Size
 W/C
 Cement content
27

28. Example 2 Batch Quantities
 Batch size contains 20 lbs of cement
 Mixing Water: 20 lbs x 0.50 = 10 lbs (values entered
as initial weights, Col 2)
 FA & CA (SSD) proportions used from mixes used to
develop graph above
 Mixing continues until a workable concrete of 3-in
slump is reached
 Results of slump, air, unit weight, and description
and workability are noted on data sheet

29. Example 2 Trial Batch Data
 Workability: (from data sheet) The amounts
of FA & CA not used are recorded, Col 3,
Masses of aggregates used (Col 2 minus Col 3)
are recorded in Col 4
 Additional information on slump, water
required, cement quantities are recorded

30. Example 2 Mixture Proportions for 1
Cubic Yard
 From Col 5 of data sheet, use batch yield (volume) & density
(unit weight) for mixture proportions
 Example, Cement lbs/cu yd = 27 cuft//volume of concrete in
batch x lbs of cement in batch; % of FA is calculated; cement
content is 539 lbs/cu yd; FA aggregate is 33.5% of total
aggregate
 Air content and slump were acceptable; 28-day compressive
strengths were 4950 psi (greater than fcr )
 Mixture in Col 5, with slump and air content, 1-3-in and 3.5%
to 5.5%,respectively, now ready for submission.

31. Example 2
Trial Mixture
Data Sheet
31

32. Test Results of Laboratory Trial Mixtures for Example 2
at a W/C Ratio of 0.50, economy & workability
Fine
aggregate,
Air Cement percent of
Batch Slump content Density content, total Worka-
no. , in. percent lb/ft3 lb/yd3 aggregate bility
1 3 5.4 144 539 33.5 Good
2 2¾ 4.9 144 555 27.4 Harsh
3 2½ 5.1 144 549 35.5 Excellent
4 3 4.7 145 540 30.5 Excellent
Inch-Pound

33. Common Mix Design Mistakes
 Not varying water-cement ratio (3 point curve)
 Not monitoring slump loss during mix design
to identify false setting tendency in cement
 Not monitoring early age concrete
temperatures to identify retardation effects of
water reducers

34. Proportioning Concrete Mixes
Ordering Concrete by ASTM C94
Option A -
 manufacturer assumes responsibility for
proportions
 purchaser specifies:
 strength requirements
 durability, placeability, density requirements

35. Proportioning Concrete Mixes
Ordering Concrete by ASTM C94
Option B -
 purchaser assumes responsibility for proportions
 purchaser specifies:
 cement content
 max allowable water content
 admixtures (type and dose)

36. Proportioning Concrete Mixes
Ordering Concrete by ASTM C94
Option C -
 manufacturer assumes responsibility for
proportions with minimum allowable cement
content specified by purchaser
 purchaser specifies:
 required compressive strength
 minimum cement content
 admixtures (type and dose)