Earthwork Cut and Fill Calculations

I spent some time reviewing the earthwork sections that will appear on the construction breadth AND depth portions of the test and realized that the books are kind of confusing in their presentation of the formulas. I figured out a way that helps me to remember the formulas easily and these problems should be straightforward free points on the actual test.

First, a few definitions (these go by a lot of different names that mean the same thing).

In Situ, bank measure: soil as it is currently on-site. This is soil that has supposedly been at rest for a while. Even if it was compacted initially it has expanded gradually over to time to be at its current at-rest condition.

Bulk Size, Swell, Transport Size, Loose, Expanded, Excavated: This is soil that has been excavated and is loose. This is used to calculated the volume used while transporting or while sitting loosely in a pile.

Compacted, shrinkage: This is the final volume of the soil after it has been placed and compacted. It is less volume than the in-situ condition due to it being more compacted than when it was at rest and is much less than the in-situ volume.

Problems prompts for these will always give a shrink factor and a bulk factor.

I don't like how the books show how to use these factors, the equations I have seen have the factor on one side and a fraction on the other. I can never seem to remember what belongs in the fraction and it is confusing what goes in the numerator and denominator.

For this reason I don't even remember the division equation. It is way easier for me to remember the equations as multiplication like this:

\text{Bulk factor} * \text{in-situ volume} = \text{bulk size}

\text{Shrink factor} * \text{in-situ volume} = \text{compacted size}

Try it out. The factor (bulk OR shrink) is always applied to the in-situ volume. The output is always the final volume depending on which factor you used.

Remember, the bulk factor will make the in-situ volume larger, so it will be greater than 1. If you are given a bulk factor of 0.15, use 1.15 in the equation so that the soil becomes 15% larger.

The shrink factor will make the in-situ volume smaller, so it will be less than 1. If you are given a shrink factor of 0.20, use 0.80 in the equation so that the soil becomes 20% smaller.

This is much easier to remember and can save some valuable time on these easy problems that will be better used on harder and longer problems.

I will cover volume calculations and working with transportation of excavated soil in another write-up. These topics go hand in hand and should also be quick to remember and perform on the test.


About Conrad

I am a Civil Engineer. I work in San Diego and am preparing to take the PE Exam. I am interested in surfing, business, travelling, and spending time with my wife. Thanks!

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