Question

A sample of 90% saturated clay soil has void ratio and specific gravity of 0.8 and 2.7, respectively. The bulk unit weight of soil in N m\(^{-3}\) is __________.

• A. 10594.80
• B. 18639.00
• C. 18.64
• D. 10.60

Hint:

The bulk unit weight of soil can be calculated using the specific gravity and void ratio, along with the unit weight of water. Make sure to use consistent units when performing the calculation.

Answer 1

The Correct Option is B

The bulk unit weight \( \gamma_b \) of soil can be calculated using the formula: \[ \gamma_b = \frac{G_s (1 + e) \gamma_w}{1 + e} \] Where: - \( G_s \) is the specific gravity of soil (given as 2.7). - \( e \) is the void ratio (given as 0.8). - \( \gamma_w \) is the unit weight of water (given as \( 9.81 \times 10^3 \, \text{N/m}^3 \)). Substitute the given values into the equation: \[ \gamma_b = \frac{2.7 \times (1 + 0.8) \times 9.81 \times 10^3}{1 + 0.8} = \frac{2.7 \times 1.8 \times 9.81 \times 10^3}{1.8} = 2.7 \times 9.81 \times 10^3 = 18639.00 \, \text{N/m}^3. \] Thus, the bulk unit weight of the soil is \( 18639.00 \, \text{N/m}^3 \). So, the correct answer is (B) 18639.00.