Compaction test, RC and saturation

The dry density of each test is found from the bulk density in the 1000 cm³ mould, $\gamma_d = \dfrac{\gamma_{bulk}}{1+w}$ (here $\gamma$ is used for density in Mg/m³).

Computation of dry density

$\gamma_{bulk} = \dfrac{\text{mass (g)}}{1000\ \text{cm}^3}$ (in Mg/m³ = g/cm³)

i) Compaction curve, $\gamma_{d,max}$ and OMC

Plot $\gamma_d$ (y-axis) against $w$ (x-axis) and draw a smooth curve through the six points. The dry density rises to a peak between 12.8% and 13.6% and then falls. A parabola through the three points around the peak gives the crest at about $w = 13.1\%$ with $\gamma_d \approx 1.90$ Mg/m³.

 γd (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

• Maximum dry unit weight, $\gamma_{d,max} \approx 1.90$ Mg/m³ ($\approx 18.6$ kN/m³)
• Optimum moisture content, OMC $\approx 13.1\%$

ii) Relative compaction

Field dry unit weight:

$$\gamma_{d,field} = \frac{2.318}{1+0.35} = 1.717\ \text{Mg/m}^3$$ $$RC = \frac{\gamma_{d,field}}{\gamma_{d,max}} \times 100 = \frac{1.717}{1.90} \times 100 = 90.4\%$$

iii) Degree of saturation at $\gamma_{d,max}$

$$e = \frac{G\gamma_w}{\gamma_d} - 1 = \frac{2.7 \times 1}{1.90} - 1 = 0.421$$ $$S = \frac{wG}{e} = \frac{0.131 \times 2.7}{0.421} = 0.84$$

Answer: $\gamma_{d,max} \approx 1.90$ Mg/m³, OMC $\approx 13.1\%$; RC $\approx 90.4\%$; $S \approx 84\%$ at maximum dry density.

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 values are probably misprinted; the RC above simply follows the data as given and shows the fill is below the usual 95% requirement.