Calculate dry density from compaction test points and estimate MDD and OMC using a controlled curve-fitting workflow.
Compaction Curve, MDD and OMC Calculation
A laboratory compaction test produces paired moisture-content and density observations. The dry-density points form a compaction curve, from which maximum dry density (MDD) and optimum moisture content (OMC) are determined using the applicable test method.
Note: This is draft calculation guidance. Specimen preparation, compactive effort, curve interpretation and reporting must follow the nominated laboratory method and project specification.
Convert bulk density to dry density
For gravimetric moisture content \(w\) expressed as a decimal:
$$ \rho_d=\frac{\rho}{1+w} $$where \(\rho\) is bulk density and \(\rho_d\) is dry density. If moisture content is recorded as a percentage, it should be converted once, at the start of the calculation:
$$ w=\frac{w_{percent}}{100} $$Construct the curve
Each accepted test point should retain:
- Moisture content
- Bulk density and calculated dry density
- Specimen and mould identifiers
- Compaction method and compactive effort
- Any exclusion or correction reason
The points should be plotted before a peak is estimated. A curve must not be extrapolated beyond the tested moisture range by default.
Optional quadratic interpolation
Where an approved procedure permits local quadratic interpolation around the peak, three or more suitable dry-density points may be fitted using:
$$ \rho_d=aw^2+bw+c $$For a concave-down curve with \(a<0\), the mathematical vertex is:
$$ OMC=-\frac{b}{2a} $$ $$ MDD=c-\frac{b^2}{4a} $$The vertex should only be reported if it lies within the approved bracketing interval and the fitted curve is appropriate for the observed data.
Illustrative example
Suppose three accepted dry-density points are:
| Moisture content | Dry density |
|---|---|
| 8% | 1.72 t/m³ |
| 10% | 1.84 t/m³ |
| 12% | 1.80 t/m³ |
A local quadratic fit gives an illustrative peak near:
$$ OMC=10.5\% $$ $$ MDD=1.845\ \text{t/m}^3 $$The result is a curve-fitting example, not a substitute for the interpretation requirements of the nominated test method.
Validation controls
- Require enough valid points on both sides of the apparent peak.
- Reject duplicate moisture values unless the repeat-test rule is defined.
- Flag a fitted vertex outside the tested range.
- Flag a positive or nearly flat quadratic coefficient.
- Preserve raw readings and excluded points.
- Do not combine results from different compactive efforts as one curve.
- Record whether MDD and OMC were measured, visually interpreted or curve-fitted.