In a previous article, we thoroughly described the procedure for ACI Concrete Mix Design. If you are not aware of the design process, go ahead and check the article.
In this article, we will give an example of ACI concrete mix design that shows you the full procedure.
ACI Concrete Mix Design: Given Data [Design Parameters]
- Concrete is for air-entrained pavement
- Pavement thickness = 25 cm
- No statistical data is available to determine the standard deviation.
- Characteristic strength (Fc’) = 34.5 MPa
- Bulk specific gravity of coarse aggregate = 2.7
- Rodded density of coarse aggregate at saturated surface dry (SSD) condition = 1650 kg/m3
- Moisture content of coarse aggregate = 1.5%
- Bulk specific gravity of fine aggregate = 2.65
- Fineness modulus of fine aggregate = 2.75
- Moisture of fine aggregate = 5% above the (SSD) condition
- Apparent specific gravity of the Portland cement = 3.15
Solution for the ACI Concrete Mix Design Problem
Step 1: Determine the Target Strength for Mix Design
Since no data is available of the concrete mix, use the following table to determine the target mean strength.
Fm = Fc’ + 8.3 = 34.5 + 8.3 = 42.8 MPa
Step 2: Select Workability Level
Workability level measured in terms of slump for the pavement is 25-75 mm
Step 3: What is the Maximum Aggregate Size
Generally speaking, it is more cost-effective to specify the greatest coarse aggregate size feasible under the design conditions. This would correspond to a 75-mm aggregate in the case of a 25-cm pavement thickness, which is on the high side but should be utilized if it is readily accessible and cost-effective. In general, the greatest size that is frequently found is a 50-mm aggregate. The maximum size stone for this design exercise will be 75 mm. Furthermore, because there must be the greatest possible traction between the pavement surface and the cars, it is preferable to specify crushed gravel when using paving concrete.
Step 4: Determine the Water-to-cement Ratio (W/C)
First, we need to determine the w/c that achieves the strength requirements from the
W/C ratio = 0.35
Note: In practice, water-reducing or superplasticizer additive would very likely have to be added in order that the concrete mix be sufficiently workable at the 0.35 w/c ratio. However, because of the fairly high percent of entrained air, the mix may still prove to be sufficiently workable. Only after the trial batch is prepared and the slump measured will the engineer (or the student) know what modification needs to be made to the mix for workability.
Compare the w/c for strength with the maximum value for durability from the following table.
Max W/C for durability = 0.45 > 0.35Then, w/c for use is 0.35
Step 5: Determine the Amount of Mixing Water and Air
The air content depends principally upon the environment under which the structure will be functioning.
First, choose the air content requirements.
The structure in this problem would qualify as a Category 1 since it is exposed to freezing/thawing so the range of air content is 4-7%.
Then from the below table, you can determine a more specific value which is 4.5% in our problem.
Air entrained concrete
| Slump | Amount of mixing water, Kg/m3
depending on the max. size of coarse aggregate (mm) |
|||||||
| 9.5 | 12.5 | 19 | 25 | 37.5 | 50 | 75 | 150 | |
| 25-50 | 181 | 175 | 168 | 160 | 150 | 142 | 122 | 107 |
| 75-100 | 202 | 193 | 184 | 175 | 165 | 157 | 133 | 119 |
| 150-175 | 216 | 205 | 197 | 184 | 174 | 166 | 154 | —- |
| Recommended air content (%) for different level of freezing-thawing exposure | ||||||||
| Mild exposure | 4.5 | 4 | 3.5 | 3 | 2.5 | 2 | 1.5 | 1 |
| Moderate exposure | 6 | 5.5 | 5 | 4.5 | 4.5 | 4 | 3.5 | 3 |
| Severe exposure | 7.5 | 7 | 6 | 6 | 5.5 | 5 | 4.5 | 4 |
It is not possible to specify and expect to repeatedly obtain an exact % of air. Furthermore, note that slightly more air is preferable to less air. Therefore, a target percent air will be chosen of -1% to +2%. In the case of this illustrative design example, a target percent of air of 5% (–1% to +2%) for a range of 4 to 7% was chosen.
Thus, air content = 5%
Also, from the previous table, the water content that achieves the target slump is 122 kg/m3
Step 5: Determine the Cement Content
Cement Content = water content / w/c ratio
= 122 / 0.35 = 349 kg/m3
The amount 349 is larger than the minimum requirements for pavements >>>> OK
Step 6: Determination of Coarse Aggregate Content
Coarse aggregate quantity is estimated from the below table based on the maximum size of coarse aggregates and the fineness modulus of the fine aggregates.
In our case, Max size is 75 mm and FM is 2.75 t
By interpolation, the volume of dry rodded coarse aggregates = 0.78
Volume of Rodded Coarse Aggregates per Unit Volume of Concrete for Different Fineness Moduli of Fine Aggregates
| Max. aggregate size (mm) | Fineness modulus of fine aggregate | |||
| 2.40 | 2.60 | 2.80 | 3 | |
| 9.5 | 0.50 | 0.48 | 0.46 | 0.44 |
| 12.5 | 0.59 | 0.57 | 0.55 | 0.53 |
| 19 | 0.66 | 0.64 | 0.62 | 0.60 |
| 25 | 0.71 | 0.69 | 0.67 | 0.65 |
| 37.5 | 0.75 | 0.73 | 0.71 | 0.69 |
| 50 | 0.78 | 0.76 | 0.74 | 0.72 |
| 76 | 0.82 | 0.80 | 0.78 | 0.76 |
For 1 m3, the amount of coarse aggregate = 0.78 * rodded density = 0.78 * 1650 = 1287 + 10% (as explained in the original post) = 1416 kg.
Step 7: Determination of Fine Aggregate Content
At this point the quantity of all the materials in the mix has been accounted for except for the fine aggregates. The latter is found by subtracting the volume of the air, cement, coarse aggregates, and water from a cubic meter to estimate the fine aggregate quantity in the batch.
Absolute volume = mass of material / [relative density of a material * density of water]
Absolute volume of cement = 349 / (3.15*1000) = 0.111 m3
Absolute volume of coarse aggregate= 1416 / (2.7*1000) = 0.524 m3
Absolute volume of water = 122 / (1*1000) = 0.122 m3
Absolute volume of air = 5% = 0.05 –> because air already given in volume.
Total volume of the above materials = 0.807 m3
Computed volume of fine aggregates = 1.000 – 0.807 = 0.193 m3
Weight of fine aggregates in the concrete batch = 0.193 × 2.65 × 1000 = 511 kg/m3
Total weight all the components in the mix (1m3) = 349 kg (cement) + 1416 kg (coarse aggregates) + 511 kg (fine aggregates) + 122 kg (water) = 2398 kg.
Now, you got everything but you need to do corrections for the moisture content in aggregates and water.
Step 8: Adjustments to consider the moisture of aggregate and trial batching
A moisture correction at this point is needed to compensate for the moisture in the aggregates above that present for the SSD condition.
The new trial batch weights are as follows:
Coarse aggregates = 1416 × (1 + moisture content /100) = 1416 * 1.015 = 1437 kg
Fine aggregates = 511 × (1 + moisture content /100) = 511* 1.05 = 537 kg
Water = 122 – 1416 × 0.015 – 511 × 0.05 = 75 kg
Cement = 349 kg
Total materials after water adjustment remains the same: 2398 kg
Trial Batching
When you do the trial batching after the ACI Concrete Mix Design, if all the targets were achieved such as the slump and air content are correct, there need be no adjustment made in the ingredients.
Otherwise, changes would have to be made in total water, air-entraining agent, and possibly the need to introduce a water-reducing additive.
In the lab, of course, we do not cast a full cubic meter of concrete You just do a small batch that gives you enough amount of concrete to do the required tests.
Let us assume you want to do a 10-kg batch, the quantities of materials will be:
Cement = 10 kg
Coarse aggregates = 10/349 × 1437 = 41.2 kg
Fine aggregates = 10/349 × 537 = 15.4 kg
Water = 10/349 × 75 = 2.1 kg
Total weight of the batch = 10 + 41.2 + 15.4 + 2.1 = 68.7 kg
As you can see, the amounts are adjusted by weight of cement in batch / total weight of cement.
Note: the amount of air-entraining agent, which is usually a liquid made from wood resin, sulfonated hydrocarbons, fatty and resinous acids, or synthetic materials, is determined from the manufacturer’s specifications and it does not matter what the amount is. All that matters is that we achieve the target air content. This will be done by trial and error based on the type of air admixture and your experience.
Two additional computations need to be made in order to adjust the batch to result in a 1-cubic-meter volume. These are the unit weight and the yield.
From the 10-kg trial batch, a bucket of 0.025 m3 was filled and weighed.
The result was 61.1 kg, which is 2444 kg/m3 (61.1 / 0.025).
So, now you have a value for the total sum of materials that we obtained previously [2398 kg].
and the value you obtained by the trial batch, which is 2444 kg
Dividing the two values gives you a value called the yield
The yield = 2398 / 2444 = 0.981 m3
This means that all of the quantities in the final mix need to be increased because the yield is less than one.
If the yield were greater than one, the weight of the ingredients would have had to be decreased.
The adjustment is done by dividing the amounts by the yield value.
The following is the final mix design adjustment:
Cement = 349.0/0.981 = 356 kg
Coarse aggregates = 1437/0.981 = 1465 kg
Fine aggregate = 537/0.981 = 565 kg
Water = 75/0.981 = 76 kg
Total weight of final adjusted materials/m3 = 2462 kg
Few Notes:
- The value we obtained is 2462 kg. In the above computations, the specific gravity of water is always assumed to be one and the density at 1000 kg/m3. However, in fact, the value differs depending on the temperature that is why we get these slight differences.
- If the specific gravity for the Portland cement has not been determined, a value of 3.15 may be used, probably without appreciable error.
- If used, the specific gravities of other cementitious materials such as fly ash, silica fume, or other pozzolans must be determined in the laboratory or obtained from the producer and considered as an additional material to the mix.
ACI Concrete Mix Design
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