Question

What is the porosity of a soil which has a bulk density of 1.33 $\text{Mg m}^{-3}$ [Pick the closest value]}

• A. 0.49 $\text{m}^3\text{ m}^{-3}$
• B. 0.53 $\text{m}^3\text{ m}^{-3}$
• C. 0.47 $\text{m}^3\text{ m}^{-3}$
• D. 0.55 $\text{m}^3\text{ m}^{-3}$

Hint:

Always memorize the default particle density value of mineral soils as \( 2.65\text{ Mg m}^{-3} \) (or \(\text{g cm}^{-3}\)) to solve bulk density-porosity conversion questions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Soil porosity ($f$ or $P$) represents the fraction of the total soil volume occupied by pores (air and water-filled spaces).
Porosity is a fundamental physical property that dictates soil compaction, water retention, aeration, and root penetration.
It is mathematically linked to two other key density parameters:
1. Bulk Density ($\rho_b$): The mass of dry soil divided by its total volume (including both solids and pore spaces).
2. Particle Density ($\rho_p$): The mass of dry soil divided by the volume of the solid soil particles only (excluding the pore space).
Key Formula or Approach:
The mathematical relationship used to calculate soil porosity from bulk density and particle density is:
\[ P = \left( 1 - \frac{\rho_b}{\rho_p} \right) \]
Where:
\( P \) is the total porosity expressed as a decimal fraction (\(\text{m}^3\text{ m}^{-3}\)).
\( \rho_b \) is the bulk density of the soil (\(\text{Mg m}^{-3}\) or \(\text{g cm}^{-3}\)).
\( \rho_p \) is the particle density of the soil (\(\text{Mg m}^{-3}\) or \(\text{g cm}^{-3}\)).
When the particle density of a typical mineral soil is not explicitly provided, it is a standard, globally accepted practice in soil science to assume an average particle density value of \( 2.65\text{ Mg m}^{-3} \) (representing the density of quartz and common silicate minerals).

Step 2: Detailed Explanation:
Let us perform the calculation step-by-step using the given bulk density value:
Given:
\[ \rho_b = 1.33\text{ Mg m}^{-3} \]
Assume:
\[ \rho_p = 2.65\text{ Mg m}^{-3} \]
Substitute these values into the porosity equation:
\[ P = 1 - \frac{1.33}{2.65} \]
First, calculate the ratio of bulk density to particle density:
\[ \frac{1.33}{2.65} \approx 0.5019 \]
Now, subtract this ratio from 1 to find the porosity:
\[ P = 1 - 0.5019 = 0.4981\text{ m}^3\text{ m}^{-3} \]
When expressed as a percentage, the porosity is approximately \( 49.8\% \).
Looking at the options provided:
(A) \( 0.49\text{ m}^3\text{ m}^{-3} \)
(B) \( 0.53\text{ m}^3\text{ m}^{-3} \)
(C) \( 0.47\text{ m}^3\text{ m}^{-3} \)
(D) \( 0.55\text{ m}^3\text{ m}^{-3} \)
The calculated value of \( 0.4981 \) is closest to \( 0.49\text{ m}^3\text{ m}^{-3} \) (or more precisely, it lies between \( 0.49 \) and \( 0.50 \)).
If we assumed a slightly lower typical particle density of \( 2.60\text{ Mg m}^{-3} \), the calculation yields:
\[ P = 1 - \frac{1.33}{2.60} = 1 - 0.5115 = 0.4885 \approx 0.49\text{ m}^3\text{ m}^{-3} \]
Thus, under standard soil mineral assumptions, the closest and most accurate value among the choices is \( 0.49\text{ m}^3\text{ m}^{-3} \).

Step 3: Final Answer:
Therefore, the porosity of the soil is \( 0.49\text{ m}^3\text{ m}^{-3} \).