# ASTM C138 - Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete

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### Density

To figure out the density, you are filling up a container with concrete. This container must have a known volume (4), minimum .20 cubic feet. First weigh the empty container (1) and record that value to the nearest tenth (.1) of a pound. After performing the proper procedures for filling the container (i.e. filling it in three lifts, mallet blows, rodding, striking off with strike-off plate), follow these steps:

### Density Calculation Steps

1. Weigh the container with the concrete (2) - record value to nearest tenth of a pound
2. Subtract the empty container weight from the full container weight (2) - (1) = weight of concrete (3)
3. Divide the weight of concrete by the known volume (3) / (4) = density, or fresh unit weight

There are a few unique procedures listed in the ASTM C138 to remember.

### Slump

1. If < 1" = Must use vibrator capable of at least 9,000 vibrations per minute
2. If 1" - 3" = Can use vibrator or tamping rod
3. If > 3" = Can’t use vibrator, only use tamping rod
• If using vibrator, fill and vibrate measure in two equal layers, not three
• Insert vibrator at three different points for each layer approx. 3 inches into the underlying layer
• Mallet mass must be 1.25 +- .5 lb for containers .5 cu.ft. or smaller
• Mallet mass 2.25 +- .5 lb for containers larger than .5 cu.ft.
• Use strike-off plate, not bar
• Metal strike-off plate dimensions - 1/4" thick
• Glass or acrylic plate dimensions - 1/2" thick

### Yield

Yield is used to determine if the concrete supplier has delivered the amount of concrete ordered.

For example, if the contractor orders 7 yards and the concrete pour comes short of filling the structure, a yield test can be performed to determine if 7 yards were actually delivered. To calculate yield, follow these simple steps. Note that you must calculate density prior to calculating yield.

You will take the total mass of all materials batched (aggregate, water, cement–this figure will be given to you on the test) to begin. The total mass of the materials is the total weight.

1. The yield per batch cu.ft. Total weight / fresh unit weight = yield per batch in feet
2. The yield per batch in cu.yds. Total weight / (fresh unit weight x 27) = yield per batch in yards
3. The yield in cu.m. Yield per batch in cu.yards x .764 = yield in cu.meters (1 cu. yd. = .764 cu. meters. This will not be on the test.)
4. The yield per cubic yard in cu.ft./cu.yd. Yield per batch [result from (a)] / cu.yds delivered = yield per cu.yd. in cu.ft./cu.yd.

Relative yield is the ratio of the actual volume of concrete obtained to the volume as designed for the batch. It is understood as a 1:1 ratio. If the relative yield calculates out to 1.00 or greater, then the yards delivered is equal to or greater than what was ordered. If it calculates to less than 1.00, then the yards delivered is less than what was ordered.

### Remember This Formula

Relative yield = yield per batch in yards (b) / cu. yds. delivered

### Air Content Calculation

Air content can be calculated in the event that your air meter does not work properly. In order to calculate this, you must have the theoretical density. This information can be obtained from the concrete supplier, who has this information on the mix design for the mix you are working with. Again, you will need your results from the fresh unit weight.

### Here's Another Formula to Remember

Theoretical Density = actual density (fresh unit weight) / theoretical x 100 = calculated air content

Since the theoretical density from the lab has no air, you are comparing that laboratory weight to the fresh weight which contains air. The air in the fresh weight sample makes it lighter than the theoretical.

The formula above allows you to subtract the fresh from the theoretical and come up with a calculated percentage of air content without performing an actual test. For the ACI test, all that is necessary is to be able to recognize the order of the formula written above.