Discussion
Determine the theoretical maximum dry density for a soil sample with specific gravity of 2.65 and optimum moisture content of 18%. (Take \(\gamma_w\) = 1 g/cm\(^3\).)
Answer: B
The theoretical maximum dry density is the dry density at the zero air voids condition, when the soil is fully saturated at the given water content:
\[ \begin{aligned} \gamma_d = \frac{G\,\gamma_w}{1 + wG} \\ &= \frac{2.65 \times 1}{1 + 0.18 \times 2.65} \\ &= \frac{2.65}{1.477} = 1.794\ \text{g/cm}^3 \end{aligned} \]The other values would come from a wrong water content or from using the formula for a different degree of saturation: 1.605 is lower and 1.832 and 1.902 are higher than the zero air voids value, which is the upper limit of the dry density at 18 percent water content.
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