The void ratio and specific gravity of a sample of clay are 0.73 and 2.7, respectively. If the voids are 92% saturated, find the bulk density, dry density and the water content. What would be the water content for complete saturation, the void ratio remaining the same?
Problem Statement (Engg. Services Exam 1998)
The void ratio and specific gravity of a clay sample are 0.73 and 2.7, respectively. At 92% saturation, calculate:
- Bulk density (\( \gamma \))
- Dry density (\( \gamma_d \))
- Water content (\( w \))
Also, determine the water content for complete saturation (void ratio remains unchanged).
Solution
1. Given Data
- Void ratio (\( e \)) = 0.73
- Specific gravity (\( G \)) = 2.7
- Saturation (\( S \)) = 92% = 0.92
- Unit weight of water (\( \gamma_w \)) = 9.81 kN/m³
2. Calculate Water Content (\( w \))
\( w = \frac{e \cdot S}{G} = \frac{0.73 \times 0.92}{2.7} = 0.2487 \, \text{or} \, 24.87\% \)
3. Calculate Dry Density (\( \gamma_d \))
\( \gamma_d = \frac{G \cdot \gamma_w}{1 + e} = \frac{2.7 \times 9.81}{1 + 0.73} = \frac{26.487}{1.73} = 15.31 \, \text{kN/m³} \)
4. Calculate Bulk Density (\( \gamma \))
\( \gamma = \gamma_d (1 + w) = 15.31 \times (1 + 0.2487) = 19.118 \, \text{kN/m³} \)
5. Water Content at Full Saturation (\( w_{\text{sat}} \))
\( w_{\text{sat}} = \frac{e}{G} = \frac{0.73}{2.7} = 0.2703 \, \text{or} \, 27.03\% \)
Results:
- Water content (\( w \)) = 24.87%
- Dry density (\( \gamma_d \)) = 15.31 kN/m³
- Bulk density (\( \gamma \)) = 19.118 kN/m³
- Water content at full saturation (\( w_{\text{sat}} \)) = 27.03%
Explanation
Key Steps:
- Water Content: Derived from the relationship between void ratio, saturation, and specific gravity.
- Dry Density: Calculated using the specific gravity, void ratio, and unit weight of water.
- Bulk Density: Combines dry density and water content to reflect the total weight of the soil.
- Full Saturation: At 100% saturation, water content depends only on void ratio and specific gravity.
Physical Meaning
1. Bulk Density (19.118 kN/m³):
- Represents the total weight of soil (solids + water) per unit volume. Critical for stability calculations in foundations.
2. Dry Density (15.31 kN/m³):
- Indicates soil compactness without water. Higher values mean better load-bearing capacity.
3. Water Content (24.87%):
- Moisture content affects compaction efficiency and shear strength. Excess water reduces soil strength.
4. Full Saturation (27.03%):
- At 100% saturation, all voids are water-filled. This is critical for assessing liquefaction risk in earthquakes.
Exam Context: Tests understanding of phase relationships and their engineering implications.
