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# Soil Terminologies | Relationships Between Soil Properties

Soil terminologies/properties cover the properties of soil that are essential in predicting the engineering behavior of soils. These properties include void ratio, water content, air content, etc. It also covers important interrelationships between these properties. Both the properties and relationship form an important part of the GATE Civil Engineering exam.

## Soil Phase Diagram

Soil is a three-phase system in general. It contains air, water, and solids as a part of the system. Soil can also exist as a two-phase system depending on the field conditions. The two-phase systems that could exist are listed below.

Dry soil system - solids and air

Saturated soil system - solids and water

Before getting into various terminologies it is important to understand certain terms related to weights and volumes of phase as listed below.

Volumes of phases

Va - Volume of air

Vw - Volume of water

Vv - Volume of voids

Vs - Volume of solids

V - Total volume of the soil mass

Weight of phases

Wa - Weight of air (zero)

Ww - Weight of water

Wv - Weight of material occupying voids (neglected)

Ws - Weight of solids

W - Total weight of the soil mass

## Soil Terminologies

### Basic Relations

There are six basic relations using weights and volumes of phases as discussed below.

#### Porosity (n)

The porosity of a soil mass is the ratio of the volume of voids to the total volume of the soil mass. It is commonly expressed as a percentage and ranges from 0 to 100%.

*n = (Vv/V) * 100 *

where,

Vv = Vw + Va

V = Vw + Va + Vs

#### Void Ratio (e)

The void ratio of a soil mass is the ratio of the volume of voids to the volume of solids in the soil mass. Its value is always greater than zero.

*e = Vv/Vs*

Void ratio is more commonly used than porosity as the volume of solids (Vs) remains constant upon application of pressure.

#### Degree of Saturation (S)

The degree of saturation of a soil mass is the ratio of the volume of water in the voids to the volume of voids. It is commonly expressed as a percentage and ranges from 0 to 100%.

*S = (Vw/Vv) * 100*

For fully saturated soil mass Vv = Vw and the degree of saturation becomes 100%. For a dry soil mass, Vw = 0, and hence the degree of saturation becomes 0.

#### Percent of Air Voids (na)

The percentage of air voids of a soil mass is the ratio of the volume of air to the total volume of soil mass. It is commonly expressed as a percentage and ranges from 0 to 100%.

*na = (Va/V) * 100*

#### Air Content (ac)

The air content of a soil mass is the ratio of the volume of air to the total volume of voids. It is commonly expressed as a percentage and ranges from 0 to 100%.

**ac = (Va/Vv) * 100**

#### Water content (w)

The water content of a soil mass is the ratio of the weight of water to the weight of solids of the soil mass. It is commonly expressed as a percentage and ranges from 0 to 100%.

*w = (Ww/Ws) * 100*

### Unit Weights of Soil

There are six unit weights that are required to be understood all of which are discussed further.

#### Bulk Unit Weight (γ)

The bulk unit weight of a soil mass is the weight per unit volume of the soil mass. It is also called the 'mass unit weight'.

**γ = W/V, **

W = Ww + Ws

V = Va + Vw + Vs

#### Unit Weight of Solids (γs)

The unit weight of solids is the weight of soil solids per unit volume of solids alone. It is also called the 'absolute unit weight'.

*γs = Ws/Vs*

#### Unit Weight of Water (γw)

The unit weight of water is the weight per unit volume of water. The unit weight of water is 9.81 kN/m^3 at 4°C which is commonly used as the standard.

*γw = Ww/Vw*

#### Saturated Unit Weight (γsat)

The saturated unit weight is nothing but the bulk unit weight in a saturated condition.

#### Submerged Unit Weight (γ')

Submerged unit weight is its unit weight in submerged condition.

**γ' = (Ws)sub/V**

**γ' = γsat - γw**

#### Dry Unit Weight (γd)

The dry unit weight of a soil mass is the soil solids per unit of total volume.

**γd = Ws/V**

### Specific Gravity of Soil

There are two specific gravity terms relating to the soil as discussed further.

#### Mass Specific Gravity (Gm)

The mass specific gravity of a soil is the ratio of mass unit weight of the soil to the unit weight of water. This is also called the 'bulk specific gravity or 'apparent specific gravity.

**Gm = ****γ/γw**

#### Specific Gravity of Solids (Gs)

The specific gravity of solids is the ratio of the unit weight of solids to the unit weight of water. It is also called the 'absolute specific gravity or 'grain specific gravity. This term is relatively constant as it is based on the unit weight of solids (γs) and hence used in almost all relations.

*Gs = γs/γw*

### Important Relations Between Soil Terminologies

Below mentioned are some of the important relations between the above-discussed terminologies. Note that G in the below relations refers to grain specific gravity i.e., Gs.

#### Void ratio and porosity

e = n/(1 - n)

n = e/(1 + e)

#### Void ratio, degree of saturation, and water content

e = wG/S

#### Air content and degree of saturation

ac = 1 - S

#### Percent of air void, porosity, and air content

na = ac * n

#### Unit weight, void ratio, grain specific gravity, and degree of saturation

γ = ((G + Se)*γw) / (1 + e)

γsat = ((G + e)*γw) / (1 + e)

γd = (G*γw) / (1+e)

γsub = (G - 1)*γw / (1 + e)

#### Dry unit weight, water content, percent of air void

γd = γbulk / (1+w)

γd = (1 - na) * ((G*γw) / (1+e))

For your easy reference, all the relations are attached as an image below which could be downloaded and used for preparation.

## Example Problem

**Question: **If the porosity of the soil sample is 20%, the void ratio is? (GATE: 1997)

**Solution:**

n = 0.2

e = n/(1 - n)

e = 0.2/0.8 = 0.25

*Therefore, the void ratio of the soil sample is 0.25*

## Practise Problem

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