Calculating Dry Unit Weight from Compaction Test Data

In soil mechanics, the compaction test is crucial for determining the relationship between the water content and the dry unit weight of a soil. This relationship helps in finding the optimum water content at which maximum dry unit weight is achieved. The dry unit weight is a fundamental property that indicates the amount of solid particles per unit volume, excluding water.

To find the dry unit weight of the compacted soil specimen, we need to follow these steps:

1. Determine the weight of the compacted soil specimen.
2. Identify the volume of the compacted soil specimen.
3. Calculate the bulk unit weight of the soil specimen.
4. Calculate the dry unit weight using the bulk unit weight and water content.

Step 1: Determine the Weight of the Compacted Soil Specimen

The total weight of the compacted soil specimen along with the mould is given. To find the weight of the soil alone, we subtract the weight of the mould.

• Weight of compacted soil specimen + mould = $38.2 \text{ N}$
• Weight of mould = $20.5 \text{ N}$
• Weight of compacted soil specimen = (Weight of soil + mould) - Weight of mould
• Weight of compacted soil specimen = $38.2 \text{ N} - 20.5 \text{ N} = 17.7 \text{ N}$

Step 2: Identify the Volume of the Compacted Soil Specimen

The volume of the compacted soil specimen is equal to the internal volume of the mould.

• Volume of mould = $0.95 \times 10^{-3} \text{ m}^3$
• Volume of compacted soil specimen = $0.95 \times 10^{-3} \text{ m}^3$

Step 3: Calculate the Bulk Unit Weight of the Soil Specimen

The bulk unit weight ($\gamma_b$) is the total weight of the soil (solids + water) per unit volume.

• Weight of compacted soil specimen = $17.7 \text{ N}$
• Volume of compacted soil specimen = $0.95 \times 10^{-3} \text{ m}^3$
• Bulk unit weight ($\gamma_b$) = $\frac{\text{Weight of compacted soil specimen}}{\text{Volume of compacted soil specimen}}$
• $\gamma_b = \frac{17.7 \text{ N}}{0.95 \times 10^{-3} \text{ m}^3}$
• $\gamma_b \approx 18631.58 \text{ N/m}^3$

It is common practice to express unit weight in $\text{kN/m}^3$. We convert from $\text{N/m}^3$ to $\text{kN/m}^3$ by dividing by 1000.

• $\gamma_b = \frac{18631.58}{1000} \text{ kN/m}^3 \approx 18.63 \text{ kN/m}^3$

Step 4: Calculate the Dry Unit Weight of the Soil Specimen

The dry unit weight ($\gamma_d$) is the weight of soil solids per unit volume. It can be calculated from the bulk unit weight and the water content ($w$) using the formula:

$\gamma_d = \frac{\gamma_b}{1 + w}$

The water content is given as 12%, which should be used as a decimal in the formula.

• Water content ($w$) = $12\% = \frac{12}{100} = 0.12$
• Bulk unit weight ($\gamma_b$) $\approx 18.63 \text{ kN/m}^3$
• Dry unit weight ($\gamma_d$) = $\frac{18.63 \text{ kN/m}^3}{1 + 0.12}$
• $\gamma_d = \frac{18.63}{1.12} \text{ kN/m}^3$
• $\gamma_d \approx 16.63 \text{ kN/m}^3$

Comparing this result to the given options, $16.63 \text{ kN/m}^3$ is nearest to $16.6 \text{ kN/m}^3$.

Summary of Calculations

Revision Table: Soil Compaction Test Concepts

Additional Information: Significance of Dry Unit Weight in Geotechnical Engineering

The dry unit weight is a critical parameter in geotechnical engineering, particularly concerning soil compaction. Achieving a target dry unit weight in the field is essential for constructing stable foundations, embankments, road bases, and other earth structures. A higher dry unit weight for a given soil type generally indicates a denser, stronger, and less permeable soil mass, which is desirable for engineering purposes.

The results from a compaction test (like the one described in the question, often a Standard Proctor or Modified Proctor test) are used to create a compaction curve. This curve plots dry unit weight versus water content. The peak of this curve gives the maximum dry unit weight and the corresponding optimum water content.

Understanding how to calculate dry unit weight from measured values of weight, volume, and water content is fundamental for interpreting compaction test results and ensuring that field compaction meets design specifications.