Problem Statement
A saturated soil sample has the following properties:
- Water content (\( w \)) = 35%
- Specific gravity (\( G \)) = 2.70
Calculate:
- Dry unit weight (\( \gamma_d \))
- Saturated unit weight (\( \gamma_{\text{sat}} \))
- Submerged unit weight (\( \gamma’ \))
Solution
1. Calculate Void Ratio (\( e \))
\( e = wG = 0.35 \times 2.70 = 0.945 \)
2. Calculate Dry Unit Weight (\( \gamma_d \))
3. Calculate Saturated Unit Weight (\( \gamma_{\text{sat}} \))
4. Calculate Submerged Unit Weight (\( \gamma’ \))
- Dry unit weight (\( \gamma_d \)) = 13.63 kN/m³
- Saturated unit weight (\( \gamma_{\text{sat}} \)) = 18.41 kN/m³
- Submerged unit weight (\( \gamma’ \)) = 8.60 kN/m³
Explanation
1. Void Ratio (\( e \)):
The void ratio of 0.945 is calculated using the relationship \( e = wG \) for saturated soil. This high void ratio indicates a loose soil structure with significant pore space.
2. Dry Unit Weight (\( \gamma_d \)):
Dry unit weight represents the weight of soil solids per unit volume, excluding water. A value of 13.63 kN/m³ suggests a relatively low density, which is typical for soils with high void ratios.
3. Saturated Unit Weight (\( \gamma_{\text{sat}} \)):
The saturated unit weight of 18.41 kN/m³ includes the weight of both soil solids and water in the voids. This value is crucial for understanding the soil’s behavior under fully saturated conditions.
4. Submerged Unit Weight (\( \gamma’ \)):
The submerged unit weight of 8.60 kN/m³ represents the effective weight of the soil when it is submerged in water. This value is important for analyzing the stability of submerged soil structures.
Physical Meaning
1. Void Ratio and Soil Structure:
A void ratio of 0.945 indicates a loose soil structure with significant pore space. This high void ratio suggests that the soil is highly compressible and has low shear strength.
2. Dry Unit Weight and Soil Density:
A dry unit weight of 13.63 kN/m³ indicates a relatively low density, which is typical for soils with high void ratios. This low density affects the soil’s load-bearing capacity and its suitability for construction projects.
3. Saturated Unit Weight and Water Retention:
The saturated unit weight of 18.41 kN/m³ reflects the total weight of the soil when all voids are filled with water. This value is important for understanding the soil’s behavior under wet conditions and for designing drainage systems.
4. Submerged Unit Weight and Stability:
The submerged unit weight of 8.60 kN/m³ is crucial for analyzing the stability of submerged soil structures, such as foundations and retaining walls. This value helps in assessing the effective stress and stability of the soil under water.
