Problem Statement (Civil Services Exam 1992)
A clayey soil has:
- Saturated moisture content (\( w_{\text{sat}} \)) = 15.8%
- Specific gravity (\( G \)) = 2.72
- Initial degree of saturation (\( S_{\text{initial}} \)) = 70.8%
- Final degree of saturation (\( S_{\text{final}} \)) = 90.8%
Find the water content (\( w_{\text{final}} \)) after the soil absorbs water.
Solution
1. Calculate Initial Void Ratio (\( e \))
\( e = \frac{w_{\text{initial}} \cdot G}{S_{\text{initial}}} = \frac{0.158 \cdot 2.72}{0.708} \approx 0.607 \)
2. Determine Final Water Content (\( w_{\text{final}} \))
\( w_{\text{final}} = \frac{e \cdot S_{\text{final}}}{G} = \frac{0.607 \cdot 0.908}{2.72} \approx 0.2026 \, \text{(or 20.26%)} \)
Result:
- Final water content: \( w_{\text{final}} \approx 20.26\% \)
Explanation
Key Steps:
- The void ratio (\( e \)) is calculated using the initial water content and saturation.
- Assuming the void ratio remains constant during water absorption, the final water content is derived from the increased saturation.
Physical Meaning
1. Void Ratio Constancy:
- The soil structure remains unchanged; water replaces air in voids, increasing saturation without altering porosity.
2. Increased Water Content (15.8% → 20.26%):
- Higher saturation improves soil plasticity and reduces air voids, affecting compressibility and strength.
Exam Context: Tests understanding of soil phase relationships for applications like slope stability and foundation design.
