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Calculating Shrink/Swell

Understanding shrink and swell factors will enable you to use Propeller’s shrink/swell calculator effectively and ensure these factors are applied correctly to materials, preventing calculation errors.

Definitions

Bank vs. Loose vs. Compacted Materials

Materials can have different volumes depending on their condition or state. Here are the key definitions:

  • Banked: Material in its natural, undisturbed state in the ground.
  • Loose: Material that has been disturbed or removed from the ground, such as stockpiles or dirt loaded into a truck.
  • Compacted: Material that has been returned to the ground and compressed.

Shrink Swell Bank Loose and Compacted Example.png

These states have varying volumes in this sequence. This means compacted material will occupy the least space, and loose material will occupy the most. This is important when determining how much material you import or export from your site.

For example, Compacted < Banked < Loose.

Shrink/Swell

Shrink/Swell is the percentage or ratio used to move between the three states of material. It’s generally referred to in terms of percentage based on the material type.

  • A particular type of material may be known to swell 25% if removed from the earth.
  • That same material may also shrink by 10% if compacted.

Shrink Swell Example.png

Typically, a swell factor is associated with moving from a banked state to a loose state, and a shrink factor is associated with moving from a banked state to a compacted state.

The relationship between these material types is not always linear. This means you can’t always multiply a volume by the shrink/swell factor to obtain a new volume.

If you have compacted material, or in other words, the shrink factor has already been applied, it's proper to use the shrink factor to "undo" compaction and arrive at banked volume.

Similarly, if you have loose material, or the swell factor has already been applied, it's proper to use the swell factor to "undo" expansion and arrive at banked volume.

Formulas

Use these formulas to navigate between each state:

Loose <--> Banked

LooseVolume = BankVolume × (1+SwellFactor)

BankVolume = LooseVolume / (1+SwellFactor)

Banked <--> Compacted

BankVolume = CompactedVolume / (1−ShrinkFactor)

CompactedVolume = BankVolume × (1−ShrinkFactor)

Compacted <--> Loose

CompactedVolume = (LooseVolume * (1-ShrinkFactor)) / (1+SwellFactor)

LooseVolume = (CompactedVolume * (1+SwellFactor)) / (1-ShrinkFactor)

Some Examples when using Propeller’s Shrink/Swell calculator 

Problem 1 - Export

You have an export job where you will be cutting banked (natural) earth and then hauling off the material. You cannot use the material as fill on the site. You want to determine how much loose material will be hauled off to help estimate costs. 

Material Properties Provided in the Earthworks Report

Shrink = 10% or 0.1

Swell =25% or 0.25

Solution

  • Fly the site before work begins.
  • Use Propeller to perform a survey-to-design comparison to obtain your banked, cut volume.
  • Use the Shrink/Swell factor to calculate your loose yardage.

In this example, you will be moving from banked material to loose material, so you would use the formula:

LooseVolume = BankVolume × (1+SwellFactor)

LooseVolume = BankVolume x (1+0.25)

Since Propeller can calculate the Bank Volume from the compare-to-design measurement, simply input the 1.25 in the Cut field to calculate the export with the swell factor included. The export is 189,405.9 yd3. 

Shrink Swell Export Example.png

Problem 2 - Balanced Site

You are dealing with what’s supposed to be a balanced site, but you want to verify this. You would be cutting banked (natural) earth in red and then filling the areas in blue to reach the design. Your fill would need to be compacted. 

Material Properties Provided in the Earthworks Report

Shrink = 30% or 0.3

Swell =25% or 0.25

Solution

  • Fly the site before work begins.
  • Use Propeller to perform a survey-to-design comparison to obtain your banked volume.
  • Use the Shrink/Swell factor to calculate your compacted yardage.

In this example, you will be moving from banked material to compacted material, so you would use the formula: 

CompactedVolume = BankVolume × (1−ShrinkFactor)

CompactedVolume = BankVolume x (1-0.3)

Since Propeller can calculate the Bank Volume from the compare-to-design measurement, simply input the 0.7 in the Cut field to calculate how much material you’d have if that material were to be compacted. In this example, there is an additional 311.4 yd3, which is negligible for a site this size.

Shrink Swell Balanced Site Example.png

Problem 3 - Digging a Hole and Replacing the Dirt

You need to dig a hole to repair a pipe and then backfill that same hole. You want to know how much extra material to bring in to fill the hole and achieve compaction. Assume the pipe volume is negligible.

In this example, you will ultimately be going from a banked state to a compacted state. Because of this, you will need more material than you took out to fill the hole.

Material Properties Provided in the Earthworks Report

Shrink = 10% or 0.1

Swell = 34.1% or 0.341

Solution

  • Fly the site after the hole has been dug.
  • Use Propeller to perform a survey-to-referecnce level comparison to obtain your banked volume.

The hole was measured to be 373.3 yd3 of banked material. You can input 0.9 into the Fill field of the Shrink/Swell calculator, or use the formula:

CompactedVolume = BankVolume × (1−ShrinkFactor)

CompactedVolume = 373.3 × (1−0.1)

CompactedVolume = 335.9 yd3

You can also calculate this volume by measuring the stockpile and applying the formula; CompactedVolume = (LooseVolume * (1-ShrinkFactor)) / (1+SwellFactor)

Shrink Swell Filling In Example.png

However, you still need to determine how much loose material will be needed.

Start by subtracting the compacted volume from the banked volume.

373.3 yd3 banked volume - 335.9 yd3 compacted volume = 37.3 yd3 additional compacted material is needed to fill the hole.

Assume the imported material will have the same shrink/swell factors. You now will use the formula
LooseVolume = (CompactedVolume * (1+SwellFactor)) / (1-ShrinkFactor)

LooseVolume = (37.3 yd3 * (1+0.341)) / (1-0.1)

The additional loose volume needed is 55.6 yd3

When using the Shrink/Swell calculator you need to use both the Shrink and Swell factors of the material when moving from compacted to loose material.

  • First, you need to "undo" the swell that occurred to the material when it was removed from the earth. This will provide the banked volume.
    • BankVolume = LooseVolume / (1+SwellFactor)
  • Next, apply the shrink factor of the material to the banked volume to get the compacted state.
    • CompactedVolume = BankVolume × (1−ShrinkFactor)
  • A single-step formula that takes into account both shrink and swell factors:

CompactedVolume = (LooseVolume * (1-ShrinkFactor)) / (1+SwellFactor)

This type of calculation is better done outside the Shrink/Swell calculator.

I still can't do it!

We wrote these articles to equip you with everything you need to get the job done on your own, but we understand that sometimes this isn't sufficient.

If you're stuck, you can connect with our support team by clicking the support button on the top right corner of your user portal.

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