Upon completing this section, you should be able to calculate concrete mix designs.

Before proportioning a concrete mix, you need information concerning the job, such as size and shapes of structural members, required strength of the concrete, and exposure conditions. The end use of the concrete and conditions at time of placement are additional factors to consider.


In table 6-3, one of the formulas for 3,000 psi concrete is 5.80 bags of cement per cubic yard, 233 pounds of sand (per bag of cement), 297 pounds of coarse aggregate (per bag of cement), and a water-cement ratio of 6.75 gallons of water to each bag of cement. These proportions are based on the assumption that the inert ingredients are in a saturated surface-dry condition, meaning that they contain all the water they are capable of absorbing, but no additional free water over and above this amount.

We need to point out that a saturated surface-dry condition almost never exists in the field. The amount of free water in the coarse aggregate is usually small enough to be ignored, but the ingredient proportions set forth in the specs must almost always be adjusted to allow for the existence of free water in the fine aggregate. Furthermore, since free water in the fine aggregate increases its measured volume or weight over that of the sand itself, the specified volume or weight of sand must be increased to offset the volume or weight of the water in the sand. Finally, the number of gallons of water used per sack of cement must be reduced to allow for the free water in the sand. The amount of water actually added at the mixer must be the specified amount per sack, less the amount of free water that is already in the ingredients in the mixer.


Table 6-3.-Normal Concrete

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When tables, such as table 6-3, are not available for determining quantities of material required for 1 cubic yard of concrete, a rule of thumb, known as rule 41 or 42, may be used for a rough estimation. According to this rule, it takes either 41 or 42 cubic feet of the combined dry amounts of cement, sand, and aggregates to produce 1 cubic yard of mixed concrete. Rule 41 is used to calculate the quantities of material for concrete when the size of the coarse aggregate is not over 1 inch. Rule 42 is used when the size of the coarse aggregate is not over 2 1/2 inches. Here is how it works.

As we mentioned earlier, a bag of cement contains 94 pounds by weight, or about 1 cubic foot by loose volume. A batch formula is usually based on the number of bags of cement used in the mixing machine.

For estimating the amount of dry materials needed to mix 1 cubic yard of concrete, rules 41 and 42 work in the same manner. The decision on which rule to use depends upon the size of the aggregate. Let’s say your specifications call for a 1:2:4 mix with 2-inch coarse aggregates, which means you use rule 42, First, add 1:2:4, which gives you 7. Then compute your material requirements as follows:

Adding your total dry materials, 6 + 12 + 24 = 42, so your calculations are correct.

Frequently, you will have to convert volumes in cubic feet to weights in pounds. In converting, multiply the required cubic feet of cement by 94 since 1 cubic foot, or 1 standard bag of cement, weighs 94 pounds. When using rule 41 for coarse aggregates, multiply the quantity of coarse gravel in cubic feet by 105 since the average weight of dry-compacted fine aggregate or gravel is 105 pounds per cubic feet. By rule 42, however, multiply the cubic feet of rock (1-inch-size coarse aggregate) by 100 since the average dry-compacted weight of this rock is 100 pounds per cubic foot.

A handling-loss factor is added in ordering materials for jobs. An additional 5 percent of materials is added for jobs requiring 200 or more cubic yards of concrete, and 10 percent is added for smaller jobs. This loss factor is based on material estimates after the requirements have been calculated. Additional loss factors may be added where conditions indicate the necessity for excessive handling of materials before batching.

Measuring Water

The water-measuring controls on a machine concrete mixer are described later in this chapter. Water measurement for hand mixing can be done with a 14-quart bucket, marked off on the inside in gallons, half-gallons, and quarter-gallons.

Never add water to the mix without carefully measuring the water, and always remember that the amount of water actually placed in the mix varies according to the amount of free water that is already in the aggregate. This means that if the aggregate is wet by a rainstorm, the proportion of water in the mix may have to be changed.

Measuring Aggregate

The accuracy of aggregate measurement by volume depends upon the accuracy with which the amount of "bulking," caused by moisture in the aggregate, can be determined. The amount of bulking varies not only with different moisture contents but also with different gradations. Fine sand, for example, is bulked more than coarse sand by the same moisture content. Furthermore, moisture content itself varies from time to time, and a small variation causes a large change in the amount of bulking. For these and other reasons, aggregate should be measured by weight rather than by volume whenever possible.

To make grading easier, to keep segregation low, and to ensure that each batch is uniform, you should store and measure coarse aggregate from separate piles or hoppers. The ratio of maximum to minimum particle size should not exceed 2:1 for a maximum nominal size larger than 1 inch. The ratio should not exceed 3:1 for a maximum nominal size smaller than 1 inch. A mass of aggregate with a nominal size of 1 1/2 inches to 1/4 inch, for example, should be separated into one pile or hopper containing 1 1/2-inch to 3/4-inch aggregate, and another pile or hopper containing 3/4-inch to 1/4-inch aggregate. A mass with a nominal size of 3 inches to 1/4 inch should be separated into one pile or hopper containing 3-inch to 1 1/2-inch aggregate, another containing 1 1/2-inch to 3/4-inch aggregate, and a third containing 3/4-inch to 1/4-inch aggregate.

Water-Cement Ratio

The major factor controlling strength, everything else being equal, is the amount of water used per bag of cement. Maximum strength is obtained by using just the amount of water, and no more, required for the complete hydration of the cement. As previously mentioned, however, a mix of this type maybe too dry to be workable. Concrete mix always contains more water than the amount required to attain maximum strength. The point for you to remember is that the strength of concrete decreases as the amount of extra water increases.

The specified water-cement ratio is the happy medium between the maximum possible strength of the concrete and the necessary minimum workability requirements. The strength of building concrete is expressed in terms of the compressive strength in pounds per square inch (psi) reached after a 7- or 28-day set. This is usually referred to as "probable average 7-day strength" and "probable average 28-day strength."


Slump testing is a means of measuring the consistency of concrete using a "slump cone." The cone is made of galvanized metal with an 8-inch-diameter base, a 4-inch-diameter top, and a 12-inch height. The base and the top are open and parallel to each other and at right angles to the axis of the cone (figure 6-4). A tamping rod 5/8 inch in diameter and 24 inches long is also needed. The tamping rod should be smooth and bullet-pointed. Do not use a piece of reinforcing bar (rebar).

Samples of concrete for test specimens are taken at the mixer or, in the case of ready-mixed concrete, from the transportation vehicle during discharge. The sample of concrete from which test specimens are made should be representative of the entire batch. Such samples are obtained by repeatedly passing a scoop or pail through the discharging stream of concrete, starting the sampling operation at the beginning of discharge, and repeating the operation until the entire batch is discharged. To counteract segregation when a sample must be transported to a test site, the concrete should be remixed with a shovel until it is uniform in appearance. The job location from which the sample was taken should be noted for future reference. In the case of paving concrete, samples may be taken from the batch immediately after depositing it on the subgrade. At least five samples should be taken at different times, and these samples should be thoroughly mixed to form the test specimen.

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Figure 6-4.-Measurement of slump.

When making a slump test, dampen the cone and place it on a flat, moist, nonabsorbent surface, From the sample of concrete obtained, immediately fill the cone in three layers, each approximately one-third the volume of the cone. In placing each scoop full of concrete in the cone, move the scoop around the edge of the cone as the concrete slides from the scoop. This ensures symmetrical distribution of concrete within the cone. Each layer is then "rodded in" with 25 strokes. The strokes should be distributed uniformly over the cross section of the cone and penetrate into the underlying layer. The bottom layer should be rodded throughout its depth.

If the cone becomes overfilled, use a straightedge to strike off the excess concrete flush with the top. The cone should be immediately removed from the concrete by raising it carefully in a vertical direction. The slump should be measured immediately after removing the cone. You determine the slump by measuring the difference between the height of the cone and the height of the specimen (figure 6-4). The slump should be recorded in terms of inches of subsidence of the specimen during the test.

After completing the slump measurement, gently tap the side of the mix with the tamping rod. The behavior of the concrete under this treatment is a valuable indication of the cohesiveness, workability, and placability of the mix. In a well-proportioned mix, tapping only causes it to slump lower. It doesn’t crumble apart or segregate by the dropping of larger aggregate particles to a lower level in the mix. If the concrete crumbles apart, it is oversanded. If it segregates, it is undersanded.


A mix must be workable enough to fill the form spaces completely, with the assistance of a reasonable amount of shoveling, spading, and vibrating. Since a fluid or "runny" mix does this more readily than a dry or "stiff’ mix, you can see that workability varies directly with fluidity. The workability of a mix is determined by the slump test. The amount of the slump, in inches, is the measure of the concrete’s workability—the more the slump, the higher the workability.

The slump can be controlled by a change in any one or all of the following: gradation of aggregates, proportion of aggregates, or moisture content. If the moisture content is too high, you should add more cement to maintain the proper water-cement ratio.

The desired degree of workability is attained by running a series of trial batches, using various amounts of fine to coarse aggregate, until a batch is produced that has the desired slump. Once the amount of increase or decrease in fines required to produce the desired slump is determined, the aggregate proportions, not the water proportion, should be altered in the field mix to conform. If the water proportion were changed, the water-cement ratio would be upset.

Never yield to the temptation to add more water without making the corresponding adjustment in the cement content. Also, make sure that crewmembers who are spreading a stiff mix by hand do not ease their labors by this method without telling you.

As you gain experience, you will discover that adjustments in workability can be made by making very minor changes in the amount of fine or coarse aggregate. Generally, everything else remaining equal, an increase in the proportion of fines stiffens a mix, whereas an increase in the proportion of coarse loosens a mix.


Before you alter the proportions set forth in a specification, you must find out from higher authority whether you are allowed to make any such alterations and, if you are, the permissible limits beyond which you must not go.


As previously mentioned, concrete consists of four essential ingredients: water, cement, sand, and coarse aggregate. The same mixture without aggregate is mortar. Mortar, which is used chiefly for bonding masonry units together, is discussed in a later chapter. Grout refers to a water-cement mixture called neat-cement grout and to a water-sand-cement mixture called sand-cement grout. Both mixtures are used to plug holes or cracks in concrete, to seal joints, to fill spaces between machinery bedplates and concrete foundations, and for similar plugging or sealing purposes. The consistency of grout may range from stiff (about 4 gallons of water per sack of cement) to fluid (as many as 10 gallons of water per sack of cement), depending upon the nature of the grouting job at hand.


When bagged cement is used, the field mix proportions are usually given in terms of designated amounts of fine and coarse aggregate per bag (or per 94 pounds) of cement. The amount of material that is mixed at a time is called a batch. The size of a batch is usual] y designated by the number of bags of cement it contains, such as a four-bag batch, a six-bag batch, and so forth.

The process of weighing out or measuring out the ingredients for a batch of concrete is called batching. When mixing is to be done by hand, the size of the batch depends upon the number of persons available to turn it with hand tools. When mixing is to be done by machine, the size of the batch depends upon the rated capacity of the mixer. The rated capacity of a mixer is given in terms of cubic feet of mixed concrete, not of dry ingredients.

On large jobs, the aggregate is weighed out in an aggregate batching plant (usually shortened to "batch plant"), like the one shown in figure 6-5. Whenever possible, a batch plant is located near to and used in conjunction with a crushing and screening plant. In a crushing and screening plant, stone is crushed into various particle sizes, which are then screened into separate piles. In a screening plant, the aggregate in its natural state is screened by sizes into separate piles.

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Figure 6-5.-Aggregate batching plant

The batch plant, which is usually portable and can be taken apart and moved from site to site, is generally set up adjacent to the pile of screened aggregate. The plant may include separate hoppers for several sizes of fine and coarse aggregates, or only one hopper for fine aggregate and another for coarse aggregate. It may have one or more divided hoppers, each containing two or more separate compartments for different sizes of aggregates.

Each storage hopper or storage hopper compartment can be discharged into a weigh box, which can, in turn, be discharged into a mixer or a batch truck. When a specific weight of aggregate is called for, the operator sets the weight on a beam scale. The operator then opens the discharge chute on the storage hopper. When the desired weight is reached in the weigh box, the scale beam rises and the operator closes the storage hopper discharge chute. The operator then opens the weigh box discharge chute, and the aggregate discharges into the mixer or batch truck. Batch plant aggregate storage hoppers are usually loaded with clamshell-equipped cranes.

The following guidelines apply to the operation of batch plants:

  • All personnel working in the batch plant area should wear hard hats at all times.
  • While persons are working in conveyor line areas, the switches and controls should be secured and tagged so that no one can engage them until all personnel are clear.
  • When hoppers are being loaded, personnel should stay away from the area of falling aggregate.
  • The scale operator should be the only person on the scale platform during batching operations.
  • Housekeeping of the charging area is important. Personnel should do everything possible to keep the area clean and free of spoiled material or overflow.
  • Debris in aggregate causes much of the damage to conveyors. Keep the material clean at all times.
  • When batch operations are conducted at night, good lighting is a must.
  • Personnel working in batch plants should use good eye hygiene. Continual neglect of eye care can have serious consequences.