Question

Mass and volume of a fully dried soil sample are 500 g and 250 cm\(^3\), respectively. The average density of the particles in the soil sample is 2.5 g/cm\(^3\). The void ratio of the soil sample is _________ %.

Hint:

The void ratio is a measure of the amount of void space (air or water) compared to the solid particles in the soil. It is a key parameter in geotechnical engineering.

Answer 1

Correct Answer: 25

Step 1: Calculate the volume of the soil particles.
The density of the soil particles is given as 2.5 g/cm\(^3\), and the mass of the soil sample is 500 g. The volume of the particles is calculated as: \[ \text{Volume of particles} = \frac{\text{Mass of particles}}{\text{Density of particles}} = \frac{500 \, \text{g}}{2.5 \, \text{g/cm}^3} = 200 \, \text{cm}^3. \] Step 2: Calculate the void volume.
The total volume of the soil sample is 250 cm\(^3\), and the volume of the particles is 200 cm\(^3\). The void volume is the difference between the total volume and the particle volume: \[ \text{Void volume} = \text{Total volume} - \text{Volume of particles} = 250 \, \text{cm}^3 - 200 \, \text{cm}^3 = 50 \, \text{cm}^3. \] Step 3: Calculate the void ratio.
The void ratio is defined as the ratio of the void volume to the volume of the soil particles: \[ \text{Void ratio} = \frac{\text{Void volume}}{\text{Volume of particles}} = \frac{50 \, \text{cm}^3}{200 \, \text{cm}^3} = 0.25. \] The void ratio expressed as a percentage is: \[ \text{Void ratio (%)} = 0.25 \times 100 = 25%. \] Step 4: Conclusion.
The void ratio of the soil sample is 25 %.