# Voids ratio porosity degree of saturation

## Learn voids ratio, porosity, degree of saturation, percentage air voids, Air content

### Voids ratio.

Voids ratio e of a given soil sample is the ratio of the volume of voids to the volume of soil solids in the given soil mass.

\[e= \frac{V_{v}}{V_{s}}\]

### Porosity.

The porosity n of a given soil sample is the ratio of the volume of voids to the total volume of the given soil mass

\[n = \frac{V_{v}}{V}\]

The voids ratio e is generally expressed as a fraction, while the porosity n is expressed as a percentage and is, therefore, also referred to as percentage voids.

Figure (a) shows the soil element in terms of voids ratio e. If the volume of voids is taken equal to e, the volume of solids, by definition equation would be equal to 1, and the total volume equal to (1 + e). Similarly, if the volume of the voids is taken equal to n [fig.(b)], the total volume of the element will be 1(unity) and hence the volume of solids would be equal to (1 – n). From Fig. (a), we have by definition of porosity

\[ n = \frac{V_{v}}{V}= \frac{e}{1+e}\]

Similarly, from Fig.(b), we get by definition of voids ratio,

\[e = \frac{V_{v}}{V_{s}} = \frac{n}{1-n}\]

Above two Equations give two relations between n and e. Combining equations we get

\[n = \frac{e}{1+e} = e(1-n)\]

### Degree of saturation.

Degree of saturation : In a given volume of voids of a sample, some space is occupied by water and the rest by air. In a fully saturated sample, the voids get completely filled with water. The degree of saturation S is defined as the ratio of the volume of water present in a given soil mass to the total volume of voids in it.Thus,

\[ s= \frac{V_{w}}{V_{v}}\]

The degree of saturation is usually expressed as a percentage and is also known as percent saturation.

For a fully saturated sample Vw = Vv and hence S = 1.

For a perfectly dry sample, Vw = zero, and hence S = 0.

Depending upon degree of saturation, a soil is generally described as dry, damp, moist, etc. figure 2.3 shows such descriptive terms corresponding to various values of degree of saturation.

### Percentage air voids.

Percentage air voids na is defined as the ratio of the volume of air voids to the total volume of the soil mass and is expressed as percentage:

\[na = \frac{V_{a}}{V}\]

### Air content.

The air content ac is defined as the ratio of volume of air voids to the volume of voids:

\[ac = \frac{V_{a}}{V_{v}}\]

Since Va = Vv – Vw,

we get \[ac = 1- \frac{V_{w}}{V_{v}} = 1-S\]