How to design a concrete
mix.ACI 318 Method.
Concrete Mix Design
Mix design means the selection of suitable ingredients of concrete and their relative quantities to obtain an economical concrete with values of certain properties not less than their desired minimum values, such as
1) Workability
2) Strength
3) Durability
4) Consistency
The code criteria to be satisfied during a mix design are the maximum water /cement ratio, maximum size of aggregate and air contents within specified limits
A concrete mix design should focus on three key issues:
1). Does the mix meet the performance requirements of the specifications with respect to strength and other characteristics such as shrinkage, permeability, w/cm ratio, etc.?
2). Is the trial batch test data adequate to justify the strength?
3). Do the materials used comply with the project requirements as evidenced by test results, certifications, and product data?
Type of cement:
The type of cement is selected depending upon the required rate of gain of strength, the likelihood of chemical attack and the required thermal behavior.
Example Problem:
Data Known:
Specified strength = 20 MPa
Required Slump = 50 mm
Maximum size of aggregate = 20 mm
FM of fine aggregate = 2.20
Grading of aggregate as satisfied by by ASTM C33
SSD specific gravity of fine and coarse aggregate = 2.65
Rodded bulk density of coarse aggregate = 1600 kg/cubic m
Absorption Capacity of coarse aggregate = 0.5 %
Absorption Capacity of fine aggregate = 0.7%
Moisture Content of fine and coarse aggregate = Zero
Exposure Conditions = Normal
SOLUTION:
Step 1: Specified Strength.
The first step is the determination of specific strength
In this case the specified strength is given as 20 MPa
Step 2: Type of Cement.
Given exposure conditions are normal, so it is better to use Portland cement.
Step 3: Target Strength.
Design average strength = fcr = fc + 7.0
= 20 +7 = 27 MPa
where,
fc = Characteristic/Specified Strength of concrete.
fcr = Target strength of concrete.
Note:
Specified Strength is the result of the actual compression testing done of properly prepared, cured and tested samples.
Whereas, Target strength implies what it was supposed to be, according to its designers.
If previous statistical data is not given then, the required average strength is determined according to the ACI code as follows:
fcr ≥ fc + 7.0 MPa for fc ≤ 21 MPa
fcr ≥ fc + 8.5 MPa for fc = 21 to 35 MPa
fcr ≥ 1.1fc + 5.0 MPa for fc > 35 MPa
Step 4: Water/Cement Ratio.
Water/Cement ratio of the concrete mix will depend upon the target strength of concrete mix. The following table show the relationship between the two by proposed by ACI Code.
Average Compressive strength at 28 days (MPa) |
Effective water/cement ratio by mass for Non Air Entrained Concrete |
45
|
0.38
|
40
|
0.43
|
35
|
0.48
|
30
|
0.55
|
25
|
0.62
|
20
|
0.70
|
15
|
0.80
|
As in our case the target strength is 27 MPa for which the required water/cement ratio is not given so we will find the required value using interpolation.
Strength W/C ratio
30 MPa 0.55
27 MPa ?
25 MPa 0.62
W/C ratio = 0.55 + (0.62-0.55) / (30-25) = 0.59
Step 5:
Water Content.
The water content of cement depends upon the slump value and the maximum aggregate size. The following table shows the relationship between them as proposed by the ACI code.
Water Content.
The water content of cement depends upon the slump value and the maximum aggregate size. The following table shows the relationship between them as proposed by the ACI code.
Workability
(Slump)
|
||||||
10
|
12.5
|
20
|
25
|
40
|
||
30
– 50
|
205
|
200
|
185
|
180
|
160
|
|
80
– 100
|
225
|
215
|
200
|
195
|
175
|
|
150
– 180
|
240
|
230
|
210
|
205
|
185
|
|
Approximate Entrapped Air Content
Percent
|
3 |
2.5 |
2.0 |
1.5 |
1.0 |
|
Recommended Avg. Air Content percent for Mild Exposure Moderate Exposure Extreme Exposure |
4.5 6.0 7.5 |
4.0 5.5 7.0 |
3.5 5.0
6.0
|
3.0 4.5
6.0
|
2.5 4.5 5.5 |
|
So as in our case the mixing water content for non-air entrained concrete with a slump of 50 mm and maximum aggregate of 20 mm is 185 kg/cubic m (from table)
Step 6:
The approximate entrapped air content is 2%.
Step 7:
Cement Content.
Cement content can be calculated by the ratio between water content to W/C ratio.
Cement Content = Water Content / W/C Ratio
= 185/0.59
= 314 kg/cubic meter
Step 8:
Grading of coarse and fine aggregates satisfy the requirements as proposed by ACI.
Step 9:
Mass of Coarse Aggregate.
It depends upon maximum size of aggregate and fineness modulus of fine aggregate.
The following table shows the relation as proposed by ACI.
Maximum Size of Aggregate
|
Dry bulk volume of Rodded Coarse
Aggregate per unit volume of concrete for fineness modulus of sand of:
|
|||||||
1.6
|
1.8
|
2.0
|
2.2
|
2.4
|
2.6
|
2.8
|
3.0
|
|
10
|
0.56
|
0.55
|
0.54
|
0.52
|
0.50
|
0.48
|
0.46
|
0.44
|
12.5
|
0.65
|
0.64
|
0.63
|
0.61
|
0.59
|
0.57
|
0.55
|
0.55
|
20
|
0.72
|
0.71
|
0.70
|
0.68
|
0.66
|
0.64
|
0.62
|
0.60
|
25
|
0.77
|
0.76
|
0.73
|
0.73
|
0.71
|
0.69
|
0.67
|
0.65
|
40
|
0.81
|
0.80
|
0.79
|
0.77
|
0.75
|
0.73
|
0.71
|
0.69
|
50
|
0.84
|
0.83
|
0.82
|
0.80
|
0.78
|
0.76
|
0.74
|
0.72
|
70
|
0.86
|
0.85
|
0.85
|
0.84
|
0.82
|
0.80
|
0.78
|
0.76
|
150
|
0.91
|
0.90
|
0.89
|
0.88
|
0.87
|
0.85
|
0.86
|
0.81
|
In this case as maximum size of aggregate is 20 mm and fineness modulus of fine aggregate is 2.20 So dry bulk volume of the aggregate per unit volume of concrete = 0.68.
Volume of SSD coarse aggregate required = 0.68 cubic m/cubic m of concrete
Mass of coarse aggregate = 0.68 * 1600 (Rodded bulk density of coarse
aggregate)
Mass of coarse aggregate = 1088 kg/cubic
Step 10:
Mass of fine aggregate.
Specific gravity of fine aggregate = Yf = 2.65
Water content = W = 185 kg/cubic m
Cement content = C = 314 kg/cubic m
Specific gravity of cement = Y = 3.15
Mass of coarse aggregate = Ac = 1088 kg/cubic m
Specific gravity of coarse aggregate = Yc = 2.65
Air content = 2 %
Mass of fine aggregate = Yf [ 1000- ( W + C/Y + Ac/Yc + 10A )]
= 2.65 [1000- ( 185 + 314/3.15 + 1088/2.65 + 20 )]
= 755 kg/cubic m
Step 11:
Extra water required for absorption of Aggregate = 0.005 * 1088 (Ac) + 0.007 * 755 (Af)
= 10.73 kg/cubic m
Total water content = 185 + 10.73 = 196 kg/cubic m
Note:
If excess water is present in the aggregate the required water is to be reduced accordingly.
Step 12:
The quantities of the mix of 1.0 cubic m are as under:
Cement : 314 kg/cubic m
Fine aggregate : 755 kg/cubic m
Coarse Aggregate : 1088 kg/cubic m
Water : 196 kg/cubic m
The mix ratio is as follows :
Cement : Fine Aggregate : Coarse Aggregate = 314 : 755 : 1088
= 1 : 2.40 : 3.46
Aggregate / Cement ratio = 5.87
W/C ratio = 0.59
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