Soil Swell and Shrinkage Calculator

What are swell and shrinkage?

When soil is dug out, air enters between the particles and the volume increases. This is swell. When the same soil is spread in a fill and rolled, it usually ends up denser than it was in the ground, so the volume decreases. This is shrinkage. Earthworks therefore deal with three volumes:

• Bank volume: the undisturbed ground. Cut volumes taken from drawings are bank volumes.
• Loose volume: the soil after digging, as loaded on trucks. Haulage is based on it.
• Compacted volume: the volume after compaction in a fill.

Formulas

Loose volume = bank volume × (1 + swell)

Compacted volume = bank volume × (1 − shrinkage)

To find the cut needed for a fill, invert the second formula: bank volume = compacted volume / (1 − shrinkage).

Example

A cut of 200 m³ bank volume with 25 percent swell means 200 × 1.25 = 250 m³ on the trucks. Placed in a fill with 10 percent shrinkage, the same soil makes 200 × 0.90 = 180 m³ of fill.

Where do the factors come from?

Measuring is the most reliable way: with bank and loose densities known, swell = bank density / loose density − 1. The ground report or the employer's specification may also give values. Published tables only give rough ranges: about 10 to 15 percent for sand and gravel, 20 to 40 for earth and clay, 50 to 80 for blasted rock.

Limits

This tool only converts volumes. The factors depend on soil, moisture and compaction and are your inputs. For final accounts, measurements and the contract govern.