When customers estimate the amount of concrete needed for a job, they calculate the volume required. Orders for concrete are then placed based on the volume in cubic yards or cubic meters. Readymix producers, however, must batch concrete by weight. Each material is weighed on a scale before it is loaded into either a central mixing drum or a truck where it is mixed before transport to the jobsite. Many producers retain a copy of these weights (called batch tickets) for each truck that leaves their yard.
Unit Weight and Yield
Producers know exactly how much 1 cubic yard (or cubic meter) of each of their mixes weighs. This is called the unit weight of concrete. Unit weight is simply the weight of material that will fill one unit of volume. In the concrete industry, one unit of volume is usually either a cubic yard or a cubic meter. Therefore, if a producer knows the weight of the materials that were batched into a truck, he can calculate exactly how much volume that concrete will fill when placed. This is the "weight versus volume" or "unit weight" relationship.
The unit weight calculation is:
Unit Weight = Weight of Concrete ÷ Volume of Concrete
This calculation can be rearranged for volume, which is known as the yield calculation. In other words, it is the volume that a certain weight of material will yield. It is the same calculation as above, but solving for volume instead of unit weight:
Volume of Concrete = Weight of Concrete ÷ Unit Weight
Calculating Concrete Yield
To determine concrete yield, first, measure the unit weight of a concrete sample in the field. Then, use the concrete plant batch ticket to find the total weight of material that was batched into the truck. Finally, divide the total weight of the materials by the unit weight of the concrete to determine the volume of concrete that is in the truck.
Example: A concrete producer knows the weight of the materials that she has batched into a truck for a standard 4,000 psi airentrained mix design. How can she find the volume of concrete that these materials will yield?
As we know, volume and weight relationships are based on unit weight calculations. Therefore, the first step is to perform a unit weight test on the jobsite according to the procedures outlined in ASTM C 138. A container of known volume is filled with concrete that has been properly sampled from the truck according to ASTM C 172. The proper procedures for filling and consolidating this container are followed and the container is then weighed. The weight of the container is subtracted from the total weight to give the weight of the concrete sample. The volume of the container is known to be 0.25 cubic feet. If the weight of the sample was found to be 36.25 pounds, the unit weight is then:
Unit Weight = Weight of Concrete (36.25 pounds) ÷ Volume of Concrete (0.25 cubic feet) = 145.0 pounds per cubic foot
Now, we need to find the total weight of materials that were batched into the truck. From the batch ticket, we find that 5 cubic yards of concrete were batched. The total weight of cement, sand, and stone was 18,860 pounds, and 156 gallons of water were also batched. Since we know that water weighs 8.33 pounds per gallon:
156 gallons of water X 8.33 pounds per gallon = 1,300 pounds of water
Weight of all other materials = 18,860 pounds
Total Batch Weight = 20,160 pounds
Going back to the yield equation:
Volume of Concrete

= Weight of Concrete ÷ Unit Weight

Volume

= 20,160 lbs. ÷ 145 lbs. per ft.^{3}

Concrete Yield (ft.^{3})

= 139.03 ft.^{3}

Converting to cubic yards:
139.03 ft.^{3} ÷ 27 ft.^{3} per yd.^{3}

= 5.15 yd.^{3}

Concrete Yield (yd.^{3})

= 5.15 yd.^{3}



Relative yield is the actual volume divided by the design volume. It can be used to compare yields of different mixes regardless of the size of the load batched. In our example, the producer had wanted to yield 5.0 cubic yards when she batched this particular truck. She actually yielded 5.15 cubic yards. Therefore, the relative yield is:
Relative Yield

= 5.15 yd.^{3} ÷ 5.0 yd.^{3}


= 1.03

The producer is yielding 3% more than her design. (A yield of 0.97 would mean 3% less than the design.)
Quality Control
Due to inherent variations in sampling and testing procedures, it is very important that yield calculations are performed on at least three different batches of the same mix design before the decision to adjust the mix is made.
Lafarge North America is committed to providing the highest quality of technical services to our customers. If you would like more information, or would like help in adjusting your mix designs, please contact your Lafarge sales representative or technical sales engineer.