**Void Ratio**

Void ratio refers to the size of voids to the volume of solids. It is indicated

e=Vv/Vs

It is expressed as a decimal.

**Porosity**

It is the ratio of volume of voids to the total volume. It is indicated by **‘n’**

n=Vv/V

It is usually expressed as a percentage.

1/n=V/Vv= (Vv+vs)/Vv

1/n= 1+ (1/e) = (1+e)/e

n=e/ (1+e) (a)

1/e= (1/n)-1= (1-n)/n

e=n/ (1-n) (b)

In equations (a) and (b), the porosity should be expressed as a ratio and not percentage.

**Degree of saturation**

The degree of saturation is the quotient of the volume of water to the volume of voids. It is indicated by ‘S’.

S=Vw/Vv

The degree of saturation is normally expressed as a percentage. It is equal to zero when the soil is absolutely dry and 100% when the soil is fully immersed.

**Percentage air voids**

It is the ratio of volume of air to the total volume.

n_{a}= Va/V

It is also expressed as a percentage.

**Air content**

Air content is the ratio of the volume of air to the volume of voids

a_{c}= Va/Vv

Also,

n_{a}= n a_{c}

**Water content**

The water content (w) is the quotient of the mass of water to the mass of soilids

w= Mw/Ms

It is also known as the moisture content (m). It is articulated as a percentage but used as a decimal in computation.

**VOLUME-MASS RELATIONSHIPS**

**BULK MASS DENSITY**

The bulk mass density (ρ) is known as the total mass (M) per unit volume (V)

ρ=M/V

**DRY MASS DENSITY**

The dry mass density (ρ_{d}) is *known as the mass of solids per unit total volume*

*ρ _{d}=_{ }Ms/V*

*SATURATED MASS DENSITY*

The saturated mass density (ρ_{sat}) refers to the bulk density of the soil when it is fully immersed.

ρ_{sat}= Msat/V

**SUBMERGED MASS DENSITY**

When the soil is located under the water, it is known as submerged condition. The submerged mass density (ρ’) of the soil is known as the submerged mass per unit total volume.

ρ’= Msub/V

**MASS DENSITY OF SOLIDS**

The mass density of solids (ρ_{s}) is equivalent to quotient of the mass of solids to volume of solids

ρ_{s}=Ms/Vs

**VOLUME-WEIGHT RELATIONSHIPS**

- BULK UNIT WEIGHT (γ)= W/V
- DRY UNIT WEIGHT (γ
_{d)}= Ws/V - SATURATED UNIT WEIGHT (γ
_{sat}) = Wsat/V - SUBMERGED UNIT WEIGHT (γ
_{sub}or γ’) = Wsub/V - UNIT WEIGHT OF SOIL SOLIDS (γ
_{s}) = Ws/Vs

**PARTICULAR GRAVITY OF SOLIDS**

The particular gravity of soil particles (G) is defined as the ratio of weight of a given volume of solids to mass of an equivalent volume of water at 4° C.

G = ρ_{s}/ρ_{w}

The mass density of water ρ_{w at} 4°C is 1gm/ml, 1000 kg/m^{3 }or 1 Mg/m^{3}

Basic Relationships

Sl No |
Relationship in mass density |
Relationship in unit weight |

1 | n = e/(1+e) | n = e/(1+e) |

2 | e = n/(1-n) | e = n/(1-n) |

3 | n_{a} = n a_{c} |
n_{a} = n a_{c} |

4 | ρ= (G+Se)ρ_{w}/(1+e) |
γ= (G+Se) γ_{ w}/(1+e) |

5 | ρ_{d} = Gρ_{w}/(1+e) |
γ_{d} = G γ_{ w}/(1+e) |

6 | ρ_{sat} = (G+e)ρ_{w}/(1+e) |
γ_{sat} = (G+e) γ_{ w}/(1+e) |

7 | ρ’ = (G-1)ρ_{w}/(1+e) |
γ’ = (G-1) γ_{ w}/(1+e) |

8 | e = wG/s | e = wG/s |

9 | ρ_{d} = ρ/(1+w) |
γ_{d} = γ/(1+w) |

10 | ρ_{d}_{ }= (1-na)G ρ_{w}/(1+wG) |
γ_{d}_{ }= (1-na)G γ_{ w}/(1+wG) |