Question

The mass and volume of a fully dried soil sample are 2200 gm and 1100 cm³, respectively. If the specific gravity of the soil particles is 2.5 and water density is 1 gm/cm³, the void ratio of the soil is \(\underline{\hspace{1cm}}\) (round off to 2 decimal places).

Hint:

The void ratio is the ratio of the volume of voids to the volume of solids in a soil sample.

Answer 1

Correct Answer: 0.25

The void ratio \( e \) is calculated using the formula: \[ e = \frac{V_v}{V_s} \] where \( V_v \) is the volume of voids and \( V_s \) is the volume of solids. The mass of solids \( M_s = 2200 \, \text{gm} \) and the specific gravity \( G_s = 2.5 \). First, calculate the volume of solids: \[ V_s = \frac{M_s}{G_s \times \rho_w} = \frac{2200}{2.5 \times 1} = 880 \, \text{cm}^3. \] The total volume is \( V = 1100 \, \text{cm}^3 \), so the volume of voids \( V_v \) is: \[ V_v = V - V_s = 1100 - 880 = 220 \, \text{cm}^3. \] Now, calculate the void ratio: \[ e = \frac{V_v}{V_s} = \frac{220}{880} = 0.25. \] Thus, the void ratio of the soil is \( \boxed{0.25} \).