Problem Statement (Engg. Services Exam 1998)
A soil sampler with a volume of 45 cm³ is filled with a dry soil sample. When the soil is poured into a graduated cylinder, it displaces 25 cm³ of water. Calculate:
- Porosity (\( n \)) of the soil.
- Void ratio (\( e \)) of the soil.
Solution
1. Given Data
- Total volume of soil (\( V \)) = 45 cm³
- Volume of water displaced (\( V_s \)) = 25 cm³ (volume of solids)
2. Calculate Volume of Voids (\( V_v \))
\( V_v = V – V_s = 45 \, \text{cm}^3 – 25 \, \text{cm}^3 = 20 \, \text{cm}^3 \)
3. Calculate Void Ratio (\( e \))
\( e = \frac{V_v}{V_s} = \frac{20}{25} = 0.8 \)
4. Calculate Porosity (\( n \))
\( n = \frac{V_v}{V} = \frac{20}{45} = 0.444 \, \text{or} \, 44.4\% \)
Results:
- Void ratio (\( e \)) = 0.8
- Porosity (\( n \)) = 44.4%
Explanation
Key Steps:
- Volume of Solids (\( V_s \)): The displaced water volume equals the volume of soil solids because the soil is dry. Water fills the voids when submerged, but only the solids displace water.
- Volume of Voids (\( V_v \)): Calculated as the difference between total volume and solids volume.
- Void Ratio (\( e \)): Ratio of voids volume to solids volume.
- Porosity (\( n \)): Ratio of voids volume to total soil volume.
Physical Meaning
1. Void Ratio (\( e = 0.8 \)):
- Indicates that the soil has 0.8 cm³ of voids for every 1 cm³ of solids. A higher \( e \) means looser soil.
2. Porosity (\( n = 44.4\% \)):
- 44.4% of the soil’s total volume is voids. This affects permeability, compressibility, and strength.
3. Importance in Engineering:
- High porosity/void ratio soils are less stable for foundations but may drain water better.
- Used to design filters, embankments, and assess liquefaction potential.
Exam Context: Tests understanding of basic soil phase relationships and displacement methods.
