Question

A sample of silt clay has a volume of 15.0 $\text{cm}^3$, total mass of 30.0 g, a dry mass of 27.0 g and specific gravity of 2.7. The void ratio will be:}

• A. 0.3
• B. 0.4
• C. 0.5
• D. 0.6

Hint:

Always use consistent units. In CGS units, the density of water is \( 1 \text{ g/cm}^3 \), which simplifies calculations involving dry density and specific gravity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In soil mechanics, the physical properties of a soil sample can be determined using basic weight-volume relationships.
The void ratio (\( e \)) is defined as the ratio of the volume of voids (\( V_v \)) to the volume of soil solids (\( V_s \)).
It can be calculated using parameters such as dry density, specific gravity, and the density of water.
Key Formula or Approach:
The dry density (\( \rho_d \)) of a soil sample is defined as:
\[ \rho_d = \frac{M_d}{V} \]
where \( M_d \) is the dry mass and \( V \) is the total volume.
The relationship between dry density, specific gravity of soil solids (\( G_s \)), density of water (\( \rho_w \)), and void ratio (\( e \)) is given by:
\[ \rho_d = \frac{G_s \rho_w}{1 + e} \]

Step 2: Detailed Explanation:
Let us calculate the parameters step-by-step:
1. Extract the given values from the problem statement:
- Total volume, \( V = 15.0 \text{ cm}^3 \)
- Total mass, \( M = 30.0 \text{ g} \)
- Dry mass, \( M_d = 27.0 \text{ g} \)
- Specific gravity of solids, \( G_s = 2.7 \)
- Assume the standard density of water, \( \rho_w = 1.0 \text{ g/cm}^3 \).
2. Calculate the dry density of the soil:
\[ \rho_d = \frac{27.0 \text{ g}}{15.0 \text{ cm}^3} = 1.8 \text{ g/cm}^3 \]
3. Use the dry density relationship to solve for the void ratio (\( e \)):
\[ 1.8 = \frac{2.7 \times 1.0}{1 + e} \]
Rearranging the equation to solve for \( 1 + e \):
\[ 1 + e = \frac{2.7}{1.8} \]
Simplifying the fraction:
\[ 1 + e = 1.5 \]
Subtracting 1 from both sides:
\[ e = 1.5 - 1 = 0.5 \]
The void ratio of the silty clay sample is \( 0.5 \).

Step 3: Final Answer:
The void ratio of the soil sample is 0.5.