Problem Statement (Civil Services Exam 1983)
A soil sample in its moist state weighs 1624 kg/m³. After drying, it weighs 1.40 tonnes/m³. Given the specific gravity of solids (\( G \)) as 2.65, determine:
- Water content (\( w \))
- Void ratio (\( e \))
- Porosity (\( n \))
- Degree of saturation (\( S \))
Solution
1. Calculate Water Content (\( w \))
\( M_w = 1624 \, \text{kg} – 1400 \, \text{kg} = 224 \, \text{kg} \)
\( w = \frac{M_w}{M_s} \times 100 = \frac{224}{1400} \times 100 = 16\% \)
2. Calculate Void Ratio (\( e \))
\( V_s = \frac{M_s}{G \cdot \rho_w} = \frac{1400}{2.65 \times 1000} = 0.5283 \, \text{m}^3 \)
\( V_v = 1 – V_s = 1 – 0.5283 = 0.4717 \, \text{m}^3 \)
\( e = \frac{V_v}{V_s} = \frac{0.4717}{0.5283} \approx 0.893 \)
3. Calculate Porosity (\( n \))
\( n = \frac{e}{1 + e} = \frac{0.893}{1.893} \approx 0.472 \, \text{(or 47.2%)} \)
4. Calculate Degree of Saturation (\( S \))
\( S = \frac{G \cdot w}{e} = \frac{2.65 \times 0.16}{0.893} \approx 0.4749 \, \text{(or 47.5%)} \)
Results:
- Water content: \( w = 16\% \)
- Void ratio: \( e = 0.893 \)
- Porosity: \( n = 47.2\% \)
- Degree of saturation: \( S = 47.5\% \)
Explanation
Key Steps:
- Water Content: Difference between moist and dry mass gives water mass (\( M_w \)).
- Void Ratio: Volume of solids (\( V_s \)) derived from dry mass and specific gravity. Total voids (\( V_v \)) = Total volume – \( V_s \).
- Porosity: Ratio of void volume to total volume.
- Degree of Saturation: Relates water volume to total void volume using \( S = \frac{G \cdot w}{e} \).
Physical Meaning
1. Water Content (16%): Indicates moderate moisture in the soil, affecting its workability and compaction.
2. Void Ratio (0.893): High void ratio suggests loose soil structure, common in sands or poorly graded soils.
3. Porosity (47.2%): Nearly half the soil volume is voids, influencing permeability and compressibility.
4. Degree of Saturation (47.5%): Less than 50% saturation means significant air voids, making the soil partially saturated.
Exam Context: Tests understanding of phase relationships in soil mechanics, critical for geotechnical design in civil engineering.
