1. Designing and Proportioning Normal Concrete Mixtures
Chapter 9-Designing and Proportioning Normal Concrete Mixtures-EB101-7th Canadian Edition-2002

2. Factors in the Proportioning of Quality Concrete Mixtures
Workability
Durability
Strength
Appearance
Economy

3. Materials Cement Supplementary Cementing Materials Water Aggregate
Admixtures
Fibres

4. Fig Trial batching verifies that a concrete mixture meets design requirements prior to use in construction (69899, 70008)

5. Mix Characteristics Strength Water-cementing materials ratio
Aggregate size and volume
Air content
Slump and workability
Water content
Cementing materials content and type
Admixtures

6. Definitions of Exposure Classes (1)
Structurally reinforced concrete exposed to chlorides with or without freezing and thawing condition i.e. bridge and parking decks, ramps, portions of marine structures in tidal and splash zones
C-2
Non-structurally reinforced (plain) concrete exposed to chlorides and F/T. i.e. garage floors, steps, pavements, sidewalks, curbs and gutters
C-3
Continuously submerged concrete exposed to chlorides but not to F/T. i.e: underwater portions of marine structures

7. Definitions of Exposure Classes (2)
Non-structurally reinforced concrete exposed to chlorides but not to F/T i.e. underground parking slabs on ground
F-1
Concrete exposed to F/T in a saturated condition but not to chlorides. i.e. pool decks, patios, tennis courts, fresh water pools, and fresh water control structures
F-2
Concrete in an unsaturated condition exposed to F/T but not chlorides i.e. Exterior walls and columns N
Conc. not exposed to chlorides or F/T. i.e. footings and interior slabs, walls and columns

8. Requirements for Classes of Exposure
Class of
exposure
Max.
w/cm
Min. 28 d
ƒcי (MPa)
Air Content
category
C-1
C-2
C-3
C-4
F-1
F-2 N
0.40
0.45
0.50
0.55
For Str. 35 32 30 25
Design ** 1 2
1***
2***
** Use Category 1 for concrete exposed to F/T
Use Category 2 for concrete not exposed to F/T
*** Interior ice rinks slabs and freezer slabs with a steel trowel finish have been found to perform satisfactorily without entrained air.

9. Recommended Air Content Relative to Maximum Size Aggregate
category
Range in air content for conc. with indicated nominal max. sizes of coarse aggregates (%)
10 mm
14- 20mm
28-40 mm 1
6 to 9
5 to 8
4 to 7 2
3 to 6

10. Requirements for Concrete Subjected to Sulphate Attack
Exposure
Water-
soluble sulphate SO4 in soil, ( %)
Sulphate
(SO4) in groundwater, mg/L
Min. specified
56-day
comp. str.
MPa
Max. w/cm
Cementing Material to be used
S-1
Very Severe
Over 2.0
Over 10,000 35
0.40 50
S-2
Severe
0.20 to 2.00
1500 to 10,000 32
0.45
S-3 Moderate
0.10 to 0.20
150 to 1500 30
0.50
20E, 40, or 50E
Table 9-2. Requirements for Concrete Subjected to Sulphate Attack
Air content category for all exposures is 2. Exception is for steel-trowled interior slabs on grade in a non freeze thaw environment, air entrainment is not required.
Type 50E cement shall not be used in reinforced concrete exposed to both chlorides and sulphates.

11. Relationship Between W/CM and 28-d Compressive Strength
Fig Approximate relationship between compressive strength and water to cementing materials ratio for concrete using 20-mm to 28-mm nominal maximum size coarse aggregate. Strength is based on cylinders moist cured 28 days per CSA A23.2-3C. Adapted from Table 9-3, ACI 211.1, ACI 211.3, and Hover 1995.

12. Relationship between W/CM and 28- day Compressive Strength
Compressive strength at 28 days, MPa
Water-cementing materials ratio by mass
Non-air-entrained concrete
Air-entrained concrete 45
0.38
0.30 40
0.42
0.34 35
0.47
0.39 30
0.54
0.45 25
0.61
0.52 20
0.69
0.60 15
0.79
0.70
Table 9-3. Relationship Between Water to Cementing Materials Ratio and Compressive Strength of Concrete
Strength is based on cylinders moist-cured 28 days in accordance with CSA A Relationship assumes nominal maximum size aggregate of about 20 to 28 mm.
Adapted from ACI and ACI

13. Bulk Volume of Coarse Aggregate
Fig Bulk volume of coarse aggregate per unit volume of concrete. Bulk volumes are based on aggregates in a dry-rodded condition as described in CSA A A. For more workable concrete, such as may be required when placement is by pump, they may be reduced up to 10%. Adapted from Table 9-4, ACI and Hover (1995 and 1998).

14. Bulk Volume of Coarse Aggregate
Nominal Max. size of agg, (mm)
Fineness modulus of sand
2.40
2.60
2.80
3.00 10
0.50
0.48
0.46
0.44 14
0.59
0.57
0.55
0.53 20
0.66
0.64
0.62
0.60 28
0.71
0.69
0.67
0.65 40
0.75
0.73 56
0.78
0.76
0.74
0.72 80
0.82
0.80
150
0.87
0.85
0.83
0.81
Table 9-4. Bulk Volume of Coarse Aggregate Per Unit Volume of Concrete
Bulk volumes are based on aggregates in a dry-rodded condition as described in
CSA A A.
Adapted from ACI

15. Absolute Volume of Coarse Aggregate per m3 of Concrete
Given: 0.46 m3 of coarse aggregate
Bulk density = 1567 kg/m3, rodded
Relative density = 2.65
Water = 1000 kg/m3
0.46 m3 • 1567 kg/m3 = kg
Absolute volume =
715.5/(2.65 • 1000) = 0.27 m3
1 m3
0.46 m3
So the coarse aggregate is 27% of the absolute volume of the concrete

16. Water and Air Require-ments for Different Slumps and Sizes of Aggregate
Water, kilograms per cubic metre of concrete, for indicated sizes of aggregate
Slump, mm
10 mm
14 mm
20 mm
28 mm
40 mm
56mm
80 mm
150 mm
25 to 50
207
199
190
179
166
154
130
113
75 to 100
228
216
205
193
181
169
145
124
150 to 175
243
202
178
160 —
Approximate amount of entrapped air in non-air-entrained concrete, percent 3
2.5 2
1.5 1
0.5
0.3
0.2
Table 9-5). Approximate Mixing Water and Air Content Requirements for Different Slumps and Nominal Maximum Sizes of Aggregate.
These quantities of mixing water are for use in computing cementing materials contents for trial batches. They are maximums for reasonably well-shaped angular coarse aggregates graded within limits of accepted specifications.
The slump values for concrete containing aggregates larger than 40 mm are based on slump tests made after removal of particles larger than 40 mm by wet screening.
Adapted from ACI and ACI 318. Hover (1995) presents this information in graphical form.
Non-air-entrained concrete

17. Water and Air Requirements for Differ-ent Slumps and Sizes of Aggregate
Water, kilograms per cubic metre of concrete,
for indicated sizes of aggregate
Slump, mm
10 mm
14 mm
20 mm
28 mm
40 mm
56 mm
80 mm
150 mm
25 to 50
181
175
168
160
150
142
122
107
75 to 100
202
193
184
165
157
133
119
150 to 175
216
205
197
174
166
154 ―
CSA A23.1 recommended ave.
total air content, percent
Category 1
6 to 9
5 to 8
4 to 7
Category 2
3 to 6
Table 9-5. Approximate Mixing Water and Air Content Requirements for Different Slumps and Nominal Maximum Sizes of Aggregate.
These quantities of mixing water are for use in computing cementing materials contents for trial batches. They are maximums for reasonably well-shaped angular coarse aggregates graded within limits of accepted specifications.
The slump values for concrete containing aggregates larger than 40 mm are based on slump tests made after removal of particles larger than 40 mm by wet screening.
See Table 9-1 and 9-2 for class of exposure and corresponding air content categories.
Adapted from CSA A23.1, ACI and ACI 318. Hover (1995) presents this information in graphical form.
Air-entrained concrete

18. Slump Test
Fig Slump test for consistency of concrete. Left figure illustrates a lower slump, right figure a higher slump. (69786, 69787)

19. Recommended Slump Ranges
Concrete construction
Slump, (mm)
Maximum
Minimum
Reinforced foundation walls and footings 75 25
Plain footings, caissons, and substructure walls
Beams and reinforced walls
100
Building columns
Pavements and slabs
Mass concrete
Table 9-6. Maximum slump may be increased by 25 mm for consolidation by hand methods, such as rodding and spading.
Plasticizers can safely provide higher slumps.
Adapted from ACI

20. Approx. Water Requirements for Various Agg. Sizes and Slumps
Fig Approximate water requirement for various slumps and crushed aggregate sizes for non-air-entrained concrete. Adapted from Table 9-5, ACI and Hover (1995 and 1998).

21. Approx. Water Requirements for Various Agg. Sizes and Slumps
Fig Approximate water requirement for various slumps and crushed aggregate sizes for air-entrained concrete. Adapted from Table 9-5, ACI and Hover (1995 and 1998).

22. Minimum Cementing Materials Content for Flatwork
Nominal max. size of aggregate, (mm)
Cementing materials
kg/m3 40
280 28
310 20
320 14
350 10
360
Table 9-7. Minimum Requirements of Cementing Materials for Concrete Used in Flatwork
Cementing materials quantities may need to be greater for severe exposure. For example, for deicer exposures, concrete should contain at least 335 kg/m3 of cementing materials.
Adapted from ACI 302.

23. Determination of Cement Content
Required Water Content
Cement Content =
Water-Cement Ratio
Example: air-entrained concrete mm max. size agg mm slump
w/c of 0.53
175 kg/m3 (Water)
= 330 kg /m3 of concrete
0.53 (W/C-ratio)

24. Cementing Materials Requirements for Concrete Exposed to Deicing Chemicals
Max. % (by mass) of total
cementing materials
Fly ash and natural pozzolans 25
Slag 50
Silica fume 10
Total of fly ash, slag, silica fume and natural pozzolans
Total of natural pozzolans
and silica fume 35
Table 9-8. Cementing Materials Requirements for Concrete Exposed to Deicing Chemicals
Cementing materials include portion of supplementary cementing materials in blended cements.
Total cementing materials include the summation of portland cements, blended cements, fly ash, slag, silica fume and other pozzolans.
Silica fume should not constitute more than 10% of total cementing materials and fly ash or other pozzolans shall not constitute more than 25% of cementing materials.
Adapted from ACI 318.

25. Maximum Chloride-Ion Content for Corrosion Protection
Type of member
Max. water-soluble chloride ion content in concrete, (%) by mass of cementing material
Prestressed concrete
0.06
Reinforced concrete exposed
to a moist environment or chlorides or both
0.15
Reinforced concrete exposed to neither a moist environment nor chlorides
1.00
Table 9-9. Maximum Chloride-Ion Content for Corrosion Protection
Source CSA Standard A23.1

26. Methods for Proportioning Concrete Mixtures
Water-cement ratio method
Mass method
Absolute volume method
Field experience (statistical data)
Trial mixtures

27. Proportioning from Field Data
Modification Factor for Standard Deviation ( 30 Tests)
Number of tests
Modification factor for standard deviation
Less than 15
see next slide (Table 9-11) 15
1.16 20
1.08 25
1.03
30 or more
1.00
Table Modification Factor for Standard Deviation When Less Than 30 Tests Are Available
Interpolate for intermediate numbers of tests.
Modified standard deviation to be used to determine required average strength, f'cr.
Adapted from ACI 318.

28. Proportioning from Field Data
Required Strength When Data Are Not Available to Establish a Standard Deviation
Specified compressive strength,
f'c, MPa
Required average compressive strength,
f'cr, MPa
Less than 21
f'c
21 to 35
f'c
Over 35
f'c
Table Required Average Compressive Strength When Data Are Not Available to Establish a Standard Deviation
Adapted from ACI 318.

29. Proportioning from Field Data
Required Strength When Data Are Available to Establish a Standard Deviation (CSA A23.1)
f'cr = f'c+ 1.4s
f'cr = f'c + (2.4s – 3.5 MPa)
Required Average Compressive Strength When Data Are Available to Establish a Standard Deviation.

30. Proportioning from Field Data
Required Strength When Data Are Available to Establish a Standard Deviation (ACI 318)
Specified compressive strength, f'c, MPa
Required average compressive strength, f'cr, MPa
 35
f'cr = f'c+ 1.34s
f'cr = f'c s – 3.45
Use larger value
Over 35
f'cr = 0.90f'c s
Required Average Compressive Strength When Data Are Available to Establish a Standard Deviation Adapted from ACI 318.

31. Proportioning from Field Data
Required Strength When Data Are Not Available to Establish a Standard Deviation
Specified compressive strength,
f'c, MPa
Required average compressive strength,
f'cr, MPa
Less than 21
f'c
21 to 35
f'c
Over 35
1.10f'c
Table Required Average Compressive Strength When Data Are Not Available to Establish a Standard Deviation
Adapted from ACI 318.

32. Proportioning by Trial Mixtures
Trial batching verifies that a concrete mixture meets design requirements prior to use in construction.
Photo 87_13. 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. The trial mixtures should have a slump and air content within ±20 mm and ± 0.5%, respectively, of the maximum permitted. Three cylinders for each water-cementing materials ratio should be tested at 28 days.

33. Density of Water at Various Temperatures
Temperature, °C
Density, kg/m3 16
998.93 18
998.58 20
998.19 22
997.75 24
997.27 26
996.75 28
996.20 30
995.61
Table Density of Water Versus Temperature

34. Absolute Volume Computation for Fine Aggregate Content
135
Water =
= m3
1 • 1000
435
Cement =
= m3
3.15 • 1000
7.0
Air =
= m3
100
Coarse
aggregate =
1072
= m3
2.68 • 1000
Subtotal = m3
Fine aggregate volume = = m3
Fine aggregate mass = • 2.64 • = 678 kg

35. Fig. 9-6. Trial mixture data sheet.

36. Result of Laboratory Trial Mixtures
Batch no.
Slump, mm
Air content, percent
Density,
kg/m3
Cement content, kg/m3
Fine aggregate, percent of total aggregate
Worka-bility 1 50
5.7
2341
346
28.6
Harsh 2 40
6.2
2332
337
33.3
Fair 3 45
7.5
2313
341
38.0
Good 4 36
6.8
2324
348
40.2
Table Example of Results of Laboratory Trial Mixtures
Water-Cement ratio was 0.45.

37. Relationship between Strength and Water to Cement Ratio
Fig Relationship between strength and water to cement ratio based on field and laboratory data for specific concrete ingredients.

38. Example Trial Mixtures for Air-Entrained Concrete of 80-mm to 100-mm Slump
W/C-ratio, kg per kg
Nominal maximum size of aggregate,mm
Air, %
Water, kg/m3 of concrete
Cement, kg/m3 of concrete
With fine sand, FM = 2.50
Fine aggregate in % of total aggregate
Fine aggre-gate,
kg/m3 of concrete
Coarse aggre-gate,
0.40 10
7.5
202
505 50
744
750 20 6
178
446 35
577
1071 40 5
158
395 29
518
1255
0.50
406 53
833
357 38
654
315 32
583
1225
Table Example Trial Mixtures for Air-Entrained Concrete of Medium Consistency,
80- mm to 100- mm slump

39. Relationship between:
Slump
Agg. Size
W/C
Cement content
Fig Example graphical relationship for a particular aggregate source demonstrating the relationship between slump, aggregate size, water to cement ratio, and cement content (Hover 1995).

40. Proportions to Make 1/10 m3 of Concrete for Small Jobs
Nominal maximum size coarse aggregate, mm
Air-entrained concrete
Cement, kg
Wet fine aggregate,
Wet coarse aggregate,
Water, 10 46 85 74 16 14 43 88 20 40 67
104 28 38 62
112 15 37 61
120
Table Proportions by Mass to Make One Tenth Cubic Metre of Concrete for Small Jobs
If crushed stone is used, decrease coarse aggregate by 5 kg and increase fine aggregate by 5 kg.

41. Proportions to Make 1/10 m3 of Concrete for Small Jobs
Nominal maximum size coarse aggregate, mm
Non-air-entrained concrete
Cement, kg
Wet fine aggregate,
Wet coarse aggregate,
Water, 10 46 94 74 18 14 43 85 88 20 40 75
104 16 28 38 72
112 15 37 69
120
Table Proportions by Mass to Make One Tenth Cubic Metre of Concrete for Small Jobs
If crushed stone is used, decrease coarse aggregate by 5 kg and increase fine aggregate by 5 kg.

42. Proportions by Bulk Volume of Concrete for Small Jobs
Nominal maximum size coarse aggregate, mm
Air-entrained concrete
Cement
Wet fine aggregate
Wet coarse aggregate
Water 10 1 2¼ 1½ 14 2 20 2½ 28 2¾ 40 3
Table Proportions by Bulk Volume* of Concrete for Small Jobs
The combined volume is approximately 2/3 of the sum of the original bulk volumes.

43. Proportions by Bulk Volume of Concrete for Small Jobs
Nominal maximum size coarse aggregate, mm
Non-air-entrained concrete
Cement
Wet fine aggregate
Wet coarse aggregate
Water 10 1 2½ 1½ 14 2 20 28 2¾ 40 3
Table Proportions by Bulk Volume* of Concrete for Small Jobs
The combined volume is approximately 2/3 of the sum of the original bulk volumes.

44. 
Fig Flowchart for selection and documentation of concrete proportions.

45. 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