Lets suppose that you are to determine the mix proportions for a concrete retaining wall exposed to fresh water in a severe climate. The minimum wall thickness is 10 inches, with 2 inches of concrete covering the reinforcement. The required average 28-day compressive strength is 4,600 psi. It should be noted that this average compressive strength is not the same as the design strength used for structural design but a higher figure expected to be produced on the average. For an in-depth discussion of determining how much the average strength should exceed the design strength, you should refer to Recommended Practice for Evaluation of Strength Test Results of Concrete, ACI 214.

The steps in proportioning a mix to satisfy the above requirements are as follows:

1. Determine the water-cement ratio. Table 17-1 indicates that a maximum water-cement ratio of 0.50 by weight satisfies the exposure requirements and that the concrete should be air entrained. Table 17-2 shows that a maximum water-cement ratio of approximately 0.42 by weight satisfies the strength requirements for Type IA (air-entraining) Portland cement with a compressive strength of 4,600 psi. As discussed previously, since both strength and exposure conditions are being considered, you will choose the lower of the two water-cement ratios, or 0.42.

2. Determine the maximum size of coarse aggregate. Since the maximum size of coarse aggregate must not exceed one fifth of the minimum wall thickness or three fourths of the space between the reinforcement and the surfaces, the maximum size of coarse aggregate you should use is 1 1/2 inches.

3. Determine the slump. Assuming in this case that vibration will be used to consolidate the concrete, table 17-4 shows the recommended slump to be 1 to 3 inches.

4. Determine the amount of mixing water and air content. To determine the amount of mixing water per cubic yard of concrete, use table 17-3. Using the lower half of this table, you can see that for 1 1/2-inch aggregates and a 3-inch slump, the recommended amount of mixing water is 275 pounds. You also see that for extreme exposure, the recommended air content is 5.5 percent.

NOTE: It is not normal practice to buy air-e ntraining cement (Type IA) and then add an air-entraining admixture; however, if the only cement available is Type IA and it does not give the needed air content, addition of an air-entraining admixture would be necessary to achieve frost resistance.

5. Determine the amount of cement required. Using the amount of mixing water and the water-cement ratio (Steps 1 and 4 above), the required cement content per cubic yard of concrete is 275 0.42 = 655 pounds.

6. Determine the quantity of coarse aggregate. Lets assume that the fineness modulus of sand is 2.6. Using table 17-5, you find that for 1 1/2-inch aggregate and a fineness modulus of 2.6, you should use 0.73 cubic feet of coarse aggregate on a dry-rodded basis for each cubic foot of concrete. So, for 1 cubic yard of concrete,

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Copyright permission not granted for electronic media. the volume needed is 27 x 0.73 = 19.71 cubic feet. Now, assuming that you determined the dry-rodded weight of the coarse aggregate to be 104 pounds per cubic foot, the dry weight of the aggregate is 19.71 x 104= 2,050 pounds.

7. Determine the amount of fine aggregate. Table 17-6 shows that the weight of 1 cubic yard of air-entrained concrete having 1 1/2-inch maximum size aggregate should be 3,960 pounds. From this figure you simply subtract the weight of the water (275 pounds), cement (655 pounds), and coarse aggregate (2,050 pounds) to determine the weight of the fine aggregate needed for a cubic yard of the concrete. Doing that, you find that you need 980 pounds of fine aggregate (sand).