Question

The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is 

• A. 0.35
• B. 0.78
• C. 0.87
• D. 1.28

Hint:

Always use the relation $w = \dfrac{S \cdot e}{G}$ to connect water content, saturation, specific gravity, and void ratio in soil mechanics.

Answer 1

The Correct Option is B

We know the relation: \[ w = \frac{S \cdot e}{G} \] where $w=$ water content, $S=$ degree of saturation, $e=$ void ratio, $G=$ specific gravity.

Step 1: Write known values.
$w = 0.15$ (15%)
$S = 0.50$ (50%)
$G = 2.60$

Step 2: Substitute values in formula.
\[ 0.15 = \frac{0.50 \cdot e}{2.60} \]

Step 3: Solve for $e$.
\[ e = \frac{0.15 \times 2.60}{0.50} \] \[ e = \frac{0.39}{0.50} = 0.78 \]

Final Answer:
\[ \boxed{0.78} \]