Relative compaction compares the dry density achieved in the field with a reference maximum dry density established by a nominated laboratory compaction method.
It is widely used for earthworks quality records, but the calculated percentage is only meaningful when the field result and reference result represent the same material and the project specification identifies the applicable test methods and acceptance criteria.
Relative compaction formula
Using dry density:
$$ RC = \frac{\rho_{d,\mathrm{field}}}{\rho_{d,\mathrm{max}}}\times100 $$The same ratio can be calculated with dry unit weight:
$$ RC = \frac{\gamma_{d,\mathrm{field}}}{\gamma_{d,\mathrm{max}}}\times100 $$| Symbol | Meaning | Common unit |
|---|---|---|
| \(RC\) | Relative compaction | % |
| \(\rho_{d,\mathrm{field}}\) | Field dry density | kg/m3 or t/m3 |
| \(\rho_{d,\mathrm{max}}\) | Reference maximum dry density | Same density unit |
| \(\gamma_{d,\mathrm{field}}\) | Field dry unit weight | kN/m3 |
| \(\gamma_{d,\mathrm{max}}\) | Reference maximum dry unit weight | kN/m3 |
The numerator and denominator must use the same quantity and unit. Do not divide density by unit weight.
Worked example
Assume:
- field dry density = 1.82 t/m3
- reference maximum dry density = 1.94 t/m3
At one decimal place, the relative compaction is 93.8 percent.
If the project has an explicitly nominated criterion of 95 percent, the unrounded difference is:
$$ 93.814-95.000=-1.186 $$This is 1.186 percentage points below the entered criterion. The acceptance decision must use the project specification, nominated method, lot definition, test location and unrounded result.
From wet density to dry density
A field device may provide bulk or wet density and moisture content. Dry density is then:
$$ \rho_d = \frac{\rho}{1+w} $$Here, \(w\) is a decimal. For a wet density of 2.05 t/m3 and moisture content of 12 percent:
$$ \rho_d = \frac{2.05}{1.12}=1.830\ \mathrm{t/m^3} $$The dry density can then be compared with the nominated reference MDD.
Read Soil Phase Relationships for the full density and moisture-content calculation.
Optional moisture ratio
Some project records may also compare field moisture content with a nominated reference moisture content:
$$ MR = \frac{w_{\mathrm{field}}}{w_{\mathrm{reference}}}\times100 $$A moisture ratio is separate from relative compaction. Whether it is required, how it is reported and whether a moisture range applies are project-specific matters.
Information that should accompany the result
A defensible record should retain:
- project and test location
- test depth or layer
- material or lot identification
- field density test report number
- field moisture content
- calculated field dry density
- reference MDD and OMC
- source sample and laboratory report number
- compaction method used for the reference
- applicable project criterion
- date, author and checker
- any oversize correction or method-specific adjustment
- calculation method version
Without the reference test details, the ratio may be mathematically correct but unsuitable for an acceptance decision.
Common calculation errors
Comparing wet density with MDD
MDD is a dry-density result. A wet or bulk field density must be converted to dry density before comparison.
Mixing units
The ratio is dimensionless, but the two density inputs must be expressed in compatible units.
Using the wrong reference result
Different compaction methods or materially different samples can produce different reference densities. The project specification should identify the required basis.
Applying a universal acceptance percentage
There is no responsible universal acceptance criterion for every earthworks layer. The criterion and lot assessment rules must come from the project documents or relevant authority requirements.
Rounding before comparison
Calculate and compare using full precision. Round only the displayed result.
Treating one result as representative of an entire lot
Sampling frequency, lot boundaries, retesting and statistical assessment are separate from the ratio itself.
Relative compaction is not relative density
Relative compaction compares a field dry density with a laboratory reference maximum dry density.
Relative density uses the current, maximum and minimum void ratios of granular soil:
$$ D_r = \frac{e_{\mathrm{max}}-e}{e_{\mathrm{max}}-e_{\mathrm{min}}}\times100 $$The two calculations should not be interchanged. A generic correlation between them is not reliable enough to replace the required project test method.
Review checklist
Before accepting a relative compaction calculation, confirm:
- Field dry density was calculated correctly.
- Field and reference units match.
- The reference MDD belongs to the applicable material.
- The nominated compaction method matches project requirements.
- Any method-specific corrections were applied outside this general formula where required.
- The acceptance criterion was supplied by the project, not by the calculator.
- Full precision was used for comparison.
- The calculation is traceable to the field and laboratory reports.
Related resources
- Maximum Dry Density
- Field Density Testing with a Nuclear Density Gauge
- Compaction Testing
- Earthworks Testing
- Soil Phase Relationships
Reference framework
Use the current applicable AS 1289 method, project specification and laboratory documentation for formal testing and reporting. This page explains the general ratio and does not reproduce a controlled test procedure.