Porosity of Soil Samples

Understanding the properties of soil is fundamental in various fields, especially in civil and geotechnical engineering. Two key properties that describe the volume relationships within a soil sample are its void ratio and porosity. Let's delve into how to determine the porosity when the void ratio is known.

Void Ratio and Porosity Relationship

The void ratio (\(e\)) of a soil sample is defined as the ratio of the volume of voids (\(V_v\)) to the volume of solid particles (\(V_s\)) in a given soil mass. Mathematically, it is expressed as:

\[e = \frac{V_v}{V_s}\]

The porosity (\(n\)) of a soil sample, on the other hand, is defined as the ratio of the volume of voids (\(V_v\)) to the total volume (\(V\)) of the soil mass. The total volume is the sum of the volume of voids and the volume of solid particles (\(V = V_v + V_s\)). So, porosity is:

\[n = \frac{V_v}{V} = \frac{V_v}{V_v + V_s}\]

There is a direct relationship between void ratio and porosity, which can be derived from their definitions. By dividing the numerator and denominator of the porosity formula by \(V_s\), we get:

\[n = \frac{V_v/V_s}{(V_v/V_s) + (V_s/V_s)} = \frac{e}{e + 1}\]

This formula, \(n = \frac{e}{1 + e}\), is crucial for converting void ratio to porosity.

Given Soil Sample Data

For this specific soil sample, we are provided with the following information:

• Void ratio (\(e\)) = 0.50
• Moisture content (\(w\)) = 30%

It is important to notice that while the moisture content is given, it is not required for calculating the porosity when the void ratio is already known. The formula directly relates porosity and void ratio, making the moisture content extraneous information for this particular calculation.

Calculating Soil Porosity

To find the porosity of the soil sample, we will use the established relationship formula between porosity (\(n\)) and void ratio (\(e\)).

Step 1: Identify the given void ratio.

The void ratio (\(e\)) of the soil sample is given as 0.50.

Step 2: Apply the porosity formula.

Substitute the given value of \(e\) into the formula \(n = \frac{e}{1 + e}\):

\[n = \frac{0.50}{1 + 0.50}\]

Step 3: Perform the calculation.

First, calculate the denominator:

\[1 + 0.50 = 1.50\]

Now, substitute this back into the formula:

\[n = \frac{0.50}{1.50}\]

To simplify the fraction, we can divide both the numerator and the denominator by 0.50:

\[n = \frac{0.50 \div 0.50}{1.50 \div 0.50}\]

\[n = \frac{1}{3}\]

Converting the fraction to a decimal:

\[n \approx 0.3333...\]

Rounding the result to two decimal places, the porosity is 0.33.

Final Porosity Value

The calculated porosity for the soil sample with a void ratio of 0.50 is 0.33. This means that 33% of the total volume of this soil sample is occupied by voids (empty spaces).