If the desired air content was not achieved, recheck the admixture content for proper air content and reduce or increase the mixing water by 5 pounds per cubic yard of concrete for each 1 percent by which the air content is to be increased or decreased, and recalculate the cement to maintain the same water-cement ratio. To find the most economical proportions, make more trial batches, varying the percentage of fine aggregate. In each batch, keep the water-cement ratio, aggregate gradation, air content, and slump approximately the same.

You also can proportion concrete mixtures using absolute volumes.

Determine the mix proportions for a retaining wall, using the following specifications and conditions:

Required 28-day compressive strength (fc)        3,000 psi

1. Estimate the air content. From table 17-3, the air content should be 5 percent (3/4-inch aggregate, air-entrained concrete, moderate exposure).

2. Estimate the mixing water content. From table 17-3, you should use 305 pounds of mixing water per cubic yard of concrete (3-inch slump, 3/4-inch aggregate, air-entrained concrete).

3. Determine the water-cement ratio. From table 17-2, a water-cement ratio of 0.59 will satisfy the strength requirement for 3,000 psi concrete. From table 17-1, you find that a water-cement ratio of 0.50 will satisfy the exposure conditions. Since 0.50 is the smaller of the ratios, that is what you should use.

4. Calculate the cement content. By using the weight of the mixing water content (Step 2) and the water-cement ratio (Step 3), you can determine the cement content as follows:

5. Calculate the coarse aggregate content. By using table 17-5 and interpolating between fineness moduli of 2.6 and 2.8, you find that for 3/4-inch aggregate having a fineness modulus of 2.7, the volume of dry-rodded aggregate per unit volume of concrete is 0.63. Therefore, the volume of coarse aggregate needed for 1 cubic yard of concrete is 0.63 x 27 = 17.01 cubic feet. Since the dry-rodded weight of the coarse aggregate is 102 pounds per cubic foot, then the weight of the coarse aggregate for a cubic yard of the concrete is 17.01 x 102= 1,735 pounds.

6. Calculate the absolute volumes. For one cubic yard of air-entrained concrete, the volume of the air can be determined by simply multiplying the air content by 27. For this mixture, the air content from Step 1 above is 5 percent; therefore, the volume of air is 0.05 x 27 = 1.35 cubic feet.

For the cement, water, and coarse aggregate, the absolute volumes can be calculated using the following equation:

By substitution into this formula, the absolute volumes of the cement, water, and coarse aggregate are calculated as follows:

Volume of cement (W = 610 pounds and G = 3.15) = 610 (3.15 x 62.4) = 3.10 cubic feet

7. Determine the fine aggregate content. To determine the weight of the fine aggregate needed for a cubic yard of the oncrete, you first need to add together the volumes obtained in Step 6 above. The resulting sum is then subtracted from 27 cubic feet to obtain the volume of the fine aggregate in a cubic yard of the concrete. This is shown as follows:

Now, having calculated the volume of the fine aggregate and having been given its specific gravity, you can use the formula shown in Step 6 above to solve for the weight of the fine aggregate as follows:

Weight of fine aggregate = 6.97 x 2.65 x 62.4
                                    = 1,152 pounds

8. Determine the quantities for the first trial batch. Lets assume that the size of our laboratory trial batch is 1 cubic yard. For a batch of this size, you need the following quantities of the ingredients:

Cement Type IA
= 610 pounds 94 pounds per sack 
= 6.49 sacks

If needed, more trial batches should be mixed to obtain the desired slump and air content while you keep the water-cement ratio constant.