Understanding Soil Properties: Porosity and Saturation

When studying soil mechanics, it's important to understand key properties like porosity, degree of saturation, and air voids. These properties help us characterize the soil's structure and how much air and water it holds.

• Porosity ($n$): This is a measure of the total volume of voids (empty spaces) in the soil compared to the total volume of the soil sample. It is usually expressed as a percentage or a decimal. A higher porosity means the soil has more empty space.
• Degree of Saturation ($S$): This indicates how much of the void space is filled with water. It is the ratio of the volume of water to the total volume of voids, expressed as a percentage or a decimal. A fully saturated soil has a degree of saturation of 100% (or 1), meaning all voids are filled with water. A perfectly dry soil has a degree of saturation of 0%.
• Percentage Air Voids ($n_a$): This represents the volume of air in the soil compared to the total volume of the soil sample, expressed as a percentage. It is essentially the volume of voids that are *not* filled with water, relative to the total soil volume.

Calculating Percentage Air Voids

The relationship between porosity ($n$), degree of saturation ($S$), and percentage air voids ($n_a$) is direct. The total volume of voids is given by porosity ($n$). If the voids are partially filled with water (degree of saturation $S$), the remaining portion of the voids is filled with air. The volume of air in the voids, relative to the total volume of voids, is $(1 - S)$. Therefore, the volume of air relative to the total soil volume (which is the definition of percentage air voids $n_a$) is the porosity multiplied by the fraction of voids filled with air.

The formula is:

$$n_a = n (1 - S)$$

Where $n$ and $S$ are taken as fractions (or decimals).

Applying the Formula to the Soil Sample

We are given the following values for the soil sample:

• Porosity ($n$) = 30%
• Degree of Saturation ($S$) = 78%

First, convert these percentages to decimals for use in the formula:

• $n = 30\% = \frac{30}{100} = 0.30$
• $S = 78\% = \frac{78}{100} = 0.78$

Now, substitute these values into the formula for percentage air voids ($n_a$):

$$n_a = n (1 - S)$$

$$n_a = 0.30 \times (1 - 0.78)$$

$$n_a = 0.30 \times (0.22)$$

$$n_a = 0.066$$

To express this as a percentage, multiply by 100%:

$$n_a = 0.066 \times 100\%$$

$$n_a = 6.6\%$$

Result for Percentage Air Voids

The calculated percentage air voids for the given soil sample is 6.6%.

This means that 6.6% of the total volume of the soil sample is occupied by air.