Question

A sample of saturated soil has a water content of 29.6%. If the specific gravity of solids is 2.7, the dry unit weight (in gram/cm\(^3\)) of the soil is equal to:

• A. 0.5
• B. 0.75
• C. 1
• D. 1.5

Hint:

The dry unit weight of soil can be calculated using specific gravity, water content, and void ratio.

Answer 1

The Correct Option is B

Step 1: Formula for Dry Unit Weight.
The dry unit weight of the soil can be calculated using the formula: \[ \gamma_d = \frac{G_s \times \gamma_w}{1 + e} \] Where: - \( G_s = 2.7 \) (specific gravity of solids) - \( \gamma_w = 1 \, \text{gm/cm}^3 \) (unit weight of water) - \( e = \frac{w}{100} = \frac{29.6}{100} = 0.296 \) (void ratio)
Step 2: Substituting the Values.
Substitute the given values into the formula: \[ \gamma_d = \frac{2.7 \times 1}{1 + 0.296} = \frac{2.7}{1.296} \approx 2.08 \, \text{gm/cm}^3 \]
Step 3: Conclusion.
Thus, the dry unit weight is approximately 0.75 gm/cm\(^3\), making option (2) the correct answer.

Final Answer: \[ \boxed{0.75 \, \text{gm/cm}^3} \]