# 5 Basic Volumetric Relationships in Soil Engineering Reading time: 1 minute

The five important volumetric relationships used in soil engineering are void ratio, porosity, percentage air voids, degree of saturation and air content. Each relation is mentioned and explained briefly in this article.

## 1. Void Ratio

Void ratio(e) is defined as the ratio of the volume of voids to the volume of solids. It is a unitless quantity expressed in decimals. The void ratio of coarse-grained soils is smaller than that of fine-grained soils. The value of void ratio can go above unity for some types of soils.

Where, Vv = Volume of Voids; Vs = Volume of Solids

## 2. Porosity (n)

Porosity(n) is defined as the ratio of the volume of voids to the total volume of the soil. This is also a unitless quantity that is expressed in percentage. The value of porosity cannot be greater than 100%. Porosity can be also called as percentage voids.

Where, V= Total volume of soil.

Note: Both void ratio and porosity are a measure of looseness or denseness of the soil. Lesser the value of void ratio and porosity, denser is the soil mass.

## 3. Degree of Saturation (S)

The degree of saturation(S) is defined as the ratio of the volume of water to the volume of voids. This is a unitless quantity which is expressed in percentage.

Where Vw= Volume of water; Vv = Volume of Voids.

Completely dry soil has a degree of saturation, S = 0. When the soil is completely wet, the degree of saturation, S = 100%.

## 4. Percentage of Air Voids (na)

Percentage of air voids in the soil is obtained by dividing the volume of air to the total volume. This is expressed in percentage. When the soil is fully saturated, the percentage of air voids is equal to zero.

Where Va= Volume of air.

## 5. Air Content

Air content is the ratio of the volume of air to the volume of voids. Air content is mostly represented in percentage. The value of air content is equal to zero when the soil is fully saturated.

## Relationship Between Void Ratio and Porosity

The porosity is given by,

n= Vv/V

Then, (1/n) = (V/Vv)

Total Volume of soil (V) = Volume of Voids (Vv) + Volume of Solids(Vs)

i.e V= Vv + Vs

Then, (1/n) = ( Vv+Vs)/Vv = 1 + (Vs/Vv) = 1 + (1/e) = (1+e)/e

Hence,

## Relationship Between Percentage Air Voids and Air Content

Percentage air voids na = Va/V

The above relation can be written as,