Problem Statement
The mass specific gravity (apparent specific gravity) of a soil equals 1.64. The specific gravity of solids is 2.70. Determine the voids ratio under the assumption that the soil is perfectly dry. What would be the voids ratio if the sample is assumed to have a water content of 8%?
Solution
1. Void Ratio for Dry Soil
Dry unit weight:
\( \gamma_d = G_m \cdot \gamma_w = 1.64 \cdot 9.81 = 16.09 \, \text{kN/m}^3 \)
Void ratio:
\( e = \frac{G \cdot \gamma_w}{\gamma_d} – 1 = \frac{2.70 \cdot 9.81}{16.09} – 1 = 0.646 \)
2. Void Ratio for Soil with Water Content
Total unit weight:
\( \gamma = G_m \cdot \gamma_w = 1.64 \cdot 9.81 = 16.09 \, \text{kN/m}^3 \)
Dry unit weight:
\( \gamma_d = \frac{\gamma}{1 + w} = \frac{16.09}{1 + 0.08} = 14.9 \, \text{kN/m}^3 \)
Void ratio:
\( e = \frac{G \cdot \gamma_w}{\gamma_d} – 1 = \frac{2.70 \cdot 9.81}{14.9} – 1 = 0.78 \)
Results:
- Void Ratio (Dry Soil): 0.646
- Void Ratio (Water Content 8%): 0.78
Explanation
- Dry Unit Weight: Calculated using the apparent specific gravity and the unit weight of water.
- Void Ratio: Represents the ratio of the void space to the solid space in the soil. Changes with water content as the total mass changes.
- Effect of Water Content: Increasing water content reduces the dry unit weight, increasing the void ratio.
Physical Meaning
- Soil Structure: Understanding void ratio helps in analyzing compaction and porosity of soil for construction purposes.
- Practical Relevance: Ensuring proper compaction and estimating the behavior of soil under varying moisture conditions is critical in geotechnical engineering.
