A compacted sample of soil with a bulk unit weight of 19.62 kN/m3 has a water content of 15%. What are its dry density, degree of saturation and air-content? Assume G = 2.65.

Compacted Soil Sample Analysis

Problem Statement

A compacted soil sample has the following properties:

Bulk unit weight (\( \gamma \)) = 19.62 kN/m³
Water content (\( w \)) = 15%
Specific gravity (\( G \)) = 2.65

Determine:

Dry density (\( \gamma_d \))
Degree of saturation (\( S \))
Air content (\( n_a \))

Solution

1. Calculate Dry Density (\( \gamma_d \))

\( \gamma_d = \frac{\gamma}{1 + w} = \frac{19.62}{1 + 0.15} = 17.06 \, \text{kN/m}^3 \)

2. Calculate Void Ratio (\( e \))

\( e = \frac{G \cdot \gamma_w}{\gamma_d} – 1 = \frac{2.65 \times 9.81}{17.06} – 1 = 0.52 \)

3. Calculate Degree of Saturation (\( S \))

\( S = \frac{wG}{e} \times 100 = \frac{0.15 \times 2.65}{0.52} \times 100 = 76.44\% \)

4. Calculate Air Content (\( n_a \))

\( n_a = \frac{V_a}{V_{\text{total}}} \times 100 = \frac{e(1 – S)}{1 + e} \times 100 = \frac{0.52(1 – 0.7644)}{1 + 0.52} \times 100 = 8.1\% \)

Final Results:

Dry density (\( \gamma_d \)) = 17.06 kN/m³
Degree of saturation (\( S \)) = 76.44%
Air content (\( n_a \)) = 8.1%

Explanation

1. Dry Density (\( \gamma_d \)):
Dry density represents the mass of soil solids per unit volume, excluding water. It is calculated by dividing the bulk unit weight by \( (1 + w) \), where \( w \) is the water content. A dry density of 17.06 kN/m³ indicates a moderately compacted soil.

2. Void Ratio (\( e \)):
The void ratio of 0.52 indicates the ratio of the volume of voids to the volume of solids. This value suggests a moderately dense soil structure, which is typical for compacted soils.

3. Degree of Saturation (\( S \)):
The degree of saturation of 76.44% means that 76.44% of the voids are filled with water. This partial saturation indicates that the soil is not fully saturated, and there is still room for additional water absorption.

4. Air Content (\( n_a \)):
The air content of 8.1% represents the proportion of the total volume occupied by air. This value is derived by considering the void ratio and the degree of saturation.

Physical Meaning

1. Dry Density and Compaction:
A dry density of 17.06 kN/m³ indicates that the soil has been moderately compacted. This value is important for assessing the soil’s load-bearing capacity and its suitability for construction projects.

2. Void Ratio and Soil Structure:
A void ratio of 0.52 suggests that the soil has a moderate amount of pore space. This is typical for soils that have been compacted but still retain some porosity. The void ratio directly affects the soil’s compressibility and permeability.

3. Degree of Saturation and Water Retention:
A degree of saturation of 76.44% indicates that the soil is partially saturated. This means that the soil can still absorb additional water, which is important for understanding its behavior under wet conditions. Partial saturation also affects the soil’s shear strength and stability.

4. Air Content and Compaction:
The air content of 8.1% shows that there is still some air trapped in the soil. This air can be expelled with further compaction or water addition, leading to increased density and strength.