Problem Statement
The in-situ density of an embankment, compacted at a water content of 12%, was determined using a core cutter. The empty mass of the cutter was 1286 g, and the cutter filled with soil had a mass of 3195 g. The volume of the cutter is 1000 cm3. Determine the bulk density, dry density, and degree of saturation of the embankment. If the embankment becomes fully saturated during rains, what would be its water content and saturated unit weight? Assume no volume changes in soil on saturation. Take the specific gravity of the soil as 2.70.
Solution
1. Bulk Density
Mass of soil in cutter:
\( M = M_{\text{cutter+soil}} – M_{\text{cutter empty}} = 3195 – 1286 = 1909 \, \text{g} \)
Bulk density:
\( \rho = \frac{M}{V} = \frac{1909}{1000} = 1.909 \, \text{g/cm}^3 \)
Bulk unit weight:
\( \gamma = 9.81 \cdot \rho = 9.81 \cdot 1.909 = 18.73 \, \text{kN/m}^3 \)
2. Dry Density
Dry unit weight:
\( \gamma_d = \frac{\gamma}{1 + w} = \frac{18.73}{1 + 0.12} = 16.72 \, \text{kN/m}^3 \)
3. Voids Ratio
\( e = \frac{G \cdot \gamma_w}{\gamma_d} – 1 = \frac{2.70 \cdot 9.81}{16.72} – 1 = 0.584 \)
4. Degree of Saturation
\( S = \frac{w \cdot G}{e} = \frac{0.12 \cdot 2.70}{0.584} = 0.555 = 55.5\% \)
5. At Saturation
Water content at saturation:
\( w_{\text{sat}} = \frac{e}{G} = \frac{0.584}{2.70} = 0.216 = 21.6\% \)
Saturated unit weight:
\( \gamma_{\text{sat}} = \frac{(G + e)}{1 + e} \cdot \gamma_w = \frac{(2.70 + 0.584)}{1 + 0.584} \cdot 9.81 = 20.34 \, \text{kN/m}^3 \)
Results:
- Bulk Density: 1.909 g/cm3 (18.73 kN/m3)
- Dry Density: 16.72 kN/m3
- Voids Ratio: 0.584
- Degree of Saturation: 55.5%
- Water Content at Saturation: 21.6%
- Saturated Unit Weight: 20.34 kN/m3
Explanation
- Bulk Density: The bulk density represents the overall mass of soil (solids + water) per unit volume, including voids.
- Dry Density: The dry density represents the mass of solid particles per unit volume, excluding water.
- Voids Ratio: The voids ratio describes the volume of voids (air and water) relative to the volume of solids.
- Degree of Saturation: The degree of saturation indicates the proportion of voids filled with water.
- Water Content at Saturation: This is the maximum water content the soil can hold when all voids are filled with water.
- Saturated Unit Weight: The weight of the soil when fully saturated with water.
Physical Meaning
- Soil Behavior: These calculations are crucial for understanding the load-bearing capacity and settlement characteristics of embankments under various moisture conditions.
- Practical Applications: These parameters are used in geotechnical design to ensure stability during dry and wet conditions, such as after heavy rainfall.
