# Density of Soil

It is defined as “Mass of soil per unit volume of soil”

Mathematically

Density of Soil= (Mass of Soil /Volume of soil)

It is denoted by Greek word ? (Rho)

$\rho&space;=&space;\frac{M}{V}$

It is expressed in $gm/cm^{3}$ or $kg/m^{3}$

# Unit Weight of Soil

It is defined as “the weight of soil per unit volume of soil”

Mathematically

Unit Weight of Soil= (Weight of Soil /Volume of Soil)

It is denoted by “$\gamma$

$\gamma&space;=&space;\frac{W}{V}$

It is expressed in $KN/m^{3}$

# Bulk Unit Weight of Soil

It is sometimes called Unit Weight only. It is the ratio of the total weight of soil to the total volume of soil

Mathematically

Bulk Unit Weight of Soil= (Weight of Soil/ Total Volume of Soil)

$\gamma&space;_{b}&space;=&space;\gamma&space;=\frac{W}{V}$

It is also called Moist Unit Weight

# Dry Unit Weight of Soil

It is defined as “ the weight of soil solids per unit total volume of sample”

Mathematically

Dry Unit Weight of Soil=( Weight of Soil Solids/Total Volume of Soil)

$\gamma_{d}&space;=&space;\frac{W_{d}}{V}$

Since

W = Wa + Ww + Ws = 0 + 0 + Ws = Ws = Wd ,therefore,

$\gamma&space;_{d}&space;=&space;\frac{W_{s}}{V}$

When all the voids of soil are filled with air it is called Dry Soil and Unit Weight as Dry Unit Weight e.g. Oven Dried Soil in Laboratory

# Unit Weight of Soil Solids

It is defined as “the weight of soil solid per unit total volume of soil solid”

Mathematically

Unit Weight of Soil Solid=( Weight of Soil Solids/Volume of Soil)

$\gamma&space;_{s}&space;=&space;\frac{W_{s}}{V_{s}}$

# Saturated Unit Weight

It is defined as “the total weight of saturated soil sample per units its total volume”

Mathematically

$\gamma_{sat}&space;=&space;\frac{W_{sat}}{V}$

When all the voids of soil are filled with water it is called Saturated Soil and its weight as Saturated Unit Weight

# Submerged Unit Weight

It is defined as “the submerge weight of soil per unit its total volume”

Mathematically

Submerged Unit Weight = (Submerged Weight of Soil/ Total Volume of Soil)

$\gamma_{sub}&space;=&space;\frac{W_{sub}}{V}$

According to the Archimedes’ Principle;

An object immersed in water will experience a buoyant force in upward direction causing reduction in weight

Thus soil submerged in water will thus have a unit weight

$\gamma_{sub}&space;=&space;\gamma_{sat}&space;-&space;\gamma_{w}$

# Three Phase System of Soil

A soil mass is a three phase system consisting of solid particles (soil grains), water and air. Thus four cases arises

1. Soil Particles with NO AIR and NO WATER in voids (Ideal Case i.e. 100% Compacted Soil)
2. Soil Particles with ONLY AIR in voids (Dry Soil)
3. Soil Particles with ONLY WATER in voids (Saturated Soil)
4. Soil Particles with BOTH AIR and WATER in voids (Partially Saturated Soil)

# Specific Gravity

It is defined as “the ratio of the unit weight of soil sample to the unit weight of water at standard temperature and pressure i.e. $4^{o}C$ and 1atm or 101.325kPa

OR

It is defined as “the ratio of the density of soil sample to the density of water at standard temperature and pressure i.e. $4^{o}C$ and 1atm or 101.325kPa

Mathematically

Specific Gravity =(Unit weight of Soil/Unit Weight of Water)

It is denoted by G or S.G.

$G&space;=&space;\frac{\gamma&space;_{soil}}{\gamma&space;_{w}}$

# Water Content

It is defined as “The ratio of the weight of water to the weight of solids”

Mathematically

Water Content =(Weight of Water /Weight of Solids)

It is denoted by w

$w=\frac{W_{w}}{W_{d}}*100$

As a single quantity it is expressed in percentage. In Relationships or Formulae, it is expressed in fraction

# Void Ratio

It is defined as “The ratio of the volume of voids to the volume of soil solid”. It is denoted by “e”

Mathematically

Void ratio = (Volume of Voids/Volume of Soil Solids)

$e=&space;\frac{V&space;_{v}}{V&space;_{s}}$

# Porosity

It is defined as “The ratio of the volume of voids to the total volume of soil sample”. It is denoted by “n”

Mathematically

Porosity = (Volume of Voids/Volume of Soil Sample)

$n=&space;\frac{V&space;_{v}}{V}$

# Degree of Saturation

It is the ratio of the Volume of Water to the Volume of Voids. It is denoted by “S”

Mathematically

Degree of Saturation= (Volume of Water / Volume Voids)

$S&space;=&space;\frac{V_{w}}{V_{v}}$

It is expressed in percentage and is also known as Percent Saturation
In a fully saturated sample;

Vw = Vv

Hence S = 1 or 100%

In case of dry sample Vw = 0, thus

S = 0

# Air Content

It is the ratio of Volume of Air to the Volume of Voids present in the given soil sample

Mathematically

Air Content = (Volume of Air/Volume of Voids)

$a_{c}&space;=&space;\frac{V_{a}}{V_{v}}$

Void Ratio, Porosity, Degree of Saturation and Air Content are Volume Ratios