Compaction test: curve, MDD, OMC, RC

(i) Compaction curve

Mould volume $= 1000$ cm³ = 1 litre, so bulk density $\rho = m/1000$ g/cm³ (Mg/m³), and

$$\rho_d = \frac{\rho}{1+w}, \qquad \gamma_d = \rho_d \times 9.81$$

ZAV: $\rho_{d,zav} = \dfrac{G\rho_w}{1+wG}$ with $G = 2.7$.

Plot $\rho_d$ (or $\gamma_d$) against $w$ and draw a smooth curve through the points. It rises to a peak between tests 3 and 4 and then falls, staying below the ZAV values.

 ρd (Mg/m³)
 1.90 |         *  *       <- peak ≈ 1.90 at w ≈ 13.1%
 1.86 |                *
 1.82 |      *
 1.78 |                       *
 1.74 |  *
      +--+---+---+---+---+---+--- w (%)
        11  12  13  14  15  16

From the smoothed curve (a parabola through the three points around the peak gives its crest at about $w = 13.1\%$):

• Maximum dry density $\approx 1.90$ Mg/m³, i.e. maximum dry unit weight $\approx 18.6$ kN/m³
• OMC $\approx 13.1\%$

(ii) Relative compaction

Field dry density:

$$\rho_{d,field} = \frac{2.318}{1 + 0.35} = 1.717\ \text{Mg/m}^3\ (\gamma_d = 16.84\ \text{kN/m}^3)$$ $$RC = \frac{\rho_{d,field}}{\rho_{d,max}} \times 100 = \frac{1.717}{1.90} \times 100 = 90.4\%$$

Answer: MDD $\approx 1.90$ Mg/m³ (18.6 kN/m³), OMC $\approx 13.1\%$, relative compaction $\approx 90\%$ (below the usual 95% requirement).

Note: the field data as printed are not physically consistent. At $w = 35\%$ the ZAV dry density is only $2.7/(1 + 0.35 \times 2.7) = 1.39$ Mg/m³, so a dry density of 1.717 Mg/m³ would need $S \approx 165\%$. The value is probably a misprint, but the RC above follows the data as given.