Question

The dry density (in g·cm\(^{-3}\)) and porosity (in per cent) of the soil sample, respectively, are:

• A. 1.53 and 43.50
• B. 1.53 and 77.00
• C. 1.65 and 43.50
• D. 1.65 and 77.00

Hint:

Dry density = wet density / (1 + water content). Porosity comes from void ratio using \(n = e/(1+e)\).

Answer 1

The Correct Option is A

Wet density = 1.8 g/cm³
Water content = 18%

Step 1: Compute dry density.
\[ \rho_d = \frac{\rho_w}{1 + w} = \frac{1.8}{1.18} = 1.53\ \text{g/cm}^3 \]

Step 2: Compute void ratio.
\[ e = \frac{G_s \rho_w}{\rho_d} - 1 = \frac{2.7}{1.53} - 1 = 0.7647 \]

Step 3: Porosity.
\[ n = \frac{e}{1 + e} = \frac{0.7647}{1.7647} = 0.4346 = 43.50% \]

Final Answer: (A) 1.53 and 43.50