A sand deposit has following properties in its natural state:A(i) bulk unit weight: 18.6 kN/m3, (ii) unit weight of soil solids: 26.3 kN/m3, (iii) water content: 10%.The same sand, when dumped loosely will experience a volume change of 18% due to bulking. Determinethe porosity of the sand in both the states.

Soil Mechanics Problems

Problem Statement

A sand deposit has the following properties in its natural state:

Bulk unit weight: 18.6 kN/m³
Unit weight of soil solids: 26.3 kN/m³
Water content: 10%

The same sand, when dumped loosely, experiences a volume change of 18% due to bulking. Determine the porosity of the sand in both states.

Solution

1. Calculate Porosity in Natural State \( n_1 \)

Using the formula:

\( 1 – n_1 = \frac{\gamma_1}{\gamma_s (1 + w)} \)

Substituting the values:

\( 1 – n_1 = \frac{18.6}{26.3 (1 + 0.1)} = \frac{18.6}{28.93} = 0.643 \)

Therefore:

\( n_1 = 1 – 0.643 = 0.357 = 35.7\% \)

2. Calculate Porosity in Loosely Dumped State \( n_2 \)

When dumped loosely, the volume changes by 18%. Assuming weight and water content remain constant, the relationship between volumes and porosities is:

\( 1 – n_2 = \frac{V_1 (1 – n_1)}{V_2} \)

Substituting \( V_2 = 1.18 \cdot V_1 \):

\( 1 – n_2 = \frac{1 – n_1}{1.18} = \frac{1 – 0.357}{1.18} = \frac{0.643}{1.18} = 0.545 \)

Therefore:

\( n_2 = 1 – 0.545 = 0.455 = 45.5\% \)

Results:

Porosity in natural state: \( n_1 = 35.7\% \)
Porosity in loosely dumped state: \( n_2 = 45.5\% \)

Explanation

Porosity is a measure of void space in a soil sample. It changes with volume alterations, such as compaction or loosening. In the natural state, the porosity is 35.7%, but when the sand is dumped loosely, the increase in volume due to bulking raises the porosity to 45.5%.

Physical Meaning

The increase in porosity when sand is dumped loosely is due to the bulking effect, where particles create additional voids. Understanding these changes is essential for evaluating soil behavior during transportation and placement in engineering applications.