Question

Calculate the void ratio of a soil having bulk density of 1.60 g $\text{cm}^{-3}$}

• A. 0.66
• B. 0.24
• C. 0.35
• D. 0.80

Hint:

When particle density ($PD$) is not provided for mineral soils, use the standard value of $2.65\text{ g cm}^{-3}$.
Calculate the void ratio directly using the formula: $e = \frac{PD}{BD} - 1$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In soil physics and engineering, the void ratio ($e$) and porosity ($f$) describe the volume of pore spaces relative to the solid phase of the soil.
The void ratio is the ratio of the volume of voids (pores) to the volume of soil solids.
Key Formula or Approach:
The relationship between bulk density ($BD$), particle density ($PD$), and porosity ($f$) is:
\[ f = 1 - \frac{BD}{PD} \]
The void ratio ($e$) is related to porosity ($f$) by the formula:
\[ e = \frac{f}{1 - f} \]
By substituting the expression for $f$ into this formula, we get:
\[ e = \frac{1 - \frac{BD}{PD}}{\frac{BD}{PD}} = \frac{PD}{BD} - 1 \]
If the particle density ($PD$) is not specified, we use the standard average value for mineral soils:
\[ PD = 2.65\text{ g cm}^{-3} \]

Step 2: Detailed Explanation:
Given values:
Bulk density of soil, $BD = 1.60\text{ g cm}^{-3}$.
Standard particle density, $PD = 2.65\text{ g cm}^{-3}$.
Let us calculate the void ratio ($e$) using the derived relationship:
\[ e = \frac{PD}{BD} - 1 \]
\[ e = \frac{2.65}{1.60} - 1 \]
\[ e = 1.65625 - 1 \]
\[ e \approx 0.656 \]
Rounding to two decimal places gives:
\[ e \approx 0.66 \]
Alternatively, calculating porosity ($f$) first:
\[ f = 1 - \frac{1.60}{2.65} \approx 1 - 0.6038 = 0.3962 \]
Using $f$ to find the void ratio ($e$):
\[ e = \frac{0.3962}{1 - 0.3962} = \frac{0.3962}{0.6038} \approx 0.656 \approx 0.66 \]
Both methods yield the same result.

Step 3: Final Answer:
The void ratio of the soil is 0.66, which corresponds to Option (A).