Road compaction specification, sand cone

Sand cone test: volume of the hole = mass of sand filling it / density of sand. Then the field density and water content follow. The specification requires both

• $\gamma_d \ge 0.95\,\gamma_{d,max} = 0.95 \times 1.95 = 1.8525$ Mg/m³
• $w$ within $13.5 \pm 2\%$, that is 11.5% to 15.5%

Location 1

$$V = \frac{39.51}{1.86} = 21.24\ \text{cm}^3$$ $$\gamma_{bulk} = \frac{43.86}{21.24} = 2.065\ \text{Mg/m}^3, \qquad \gamma_d = \frac{38.46}{21.24} = 1.811\ \text{Mg/m}^3$$ $$w = \frac{43.86 - 38.46}{38.46} \times 100 = 14.0\%$$ $$RC = \frac{1.811}{1.95} \times 100 = 92.8\%$$

Location 2

$$V = \frac{32.39}{1.86} = 17.41\ \text{cm}^3$$ $$\gamma_{bulk} = \frac{37.38}{17.41} = 2.147\ \text{Mg/m}^3, \qquad \gamma_d = \frac{32.21}{17.41} = 1.850\ \text{Mg/m}^3$$ $$w = \frac{37.38 - 32.21}{32.21} \times 100 = 16.05\%$$ $$RC = \frac{1.850}{1.95} \times 100 = 94.9\%$$

Comparison

Answer: The specification is not satisfied. Location 1 fails on density (RC 92.8% < 95%) though its water content is acceptable. Location 2 is just below 95% (94.9%) and its water content (16.05%) is above the 15.5% limit. Both areas need re-rolling (and drying at location 2).

The masses are taken as grams, as given; the result depends only on their ratios.