A soil mass consists of solid particles which form a porous structure. The voids in the soil mass may be filled with air, water or partly with water and partly with water. Soil is a three phase system in general.

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**VOLUMETRIC 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

**Void Ratio**

Void ratio is the volume of voids to the volume of solids. It is denoted by **‘e’**

e=Vv/Vs

It is expressed as a decimal.

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**Porosity**

It is defined as the ratio of volume of voids to the total volume. It is denoted by **‘n’**

n=Vv/V

It is generally 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.

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**Degree of saturation**

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

S=Vw/Vv

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

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**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.

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**Air content**

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

a_{c}= Va/Vv

Also,

n_{a}=n a_{c}

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**Water content**

The water content (w) is defined as the ratio of the mass of water to the mass of soilids

w= Mw/Ms

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

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**VOLUME-MASS RELATIONSHIPS**

**1. BULK MASS DENSITY**

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

ρ=M/V

**2. DRY MASS DENSITY**

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

ρ_{d}=_{ }Ms/V

**3. SATURATED MASS DENSITY**

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

ρ_{sat}= Msat/V

**4. SUBMERGED MASS DENSITY**

When the soil exists below water, it is in a submerged condition. The submerged mass density (ρ’) of the soil is defined as the submerged mass per unit total volume.

ρ’= Msub/V

**5. MASS DENSITY OF SOLIDS**

The mass density of solids (ρ_{s}) is equal to the ratio of the mass of solids to the volume of solids

ρ_{s}=Ms/Vs

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**VOLUME-WEIGHT RELATIONSHIPS**

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**SPECIFIC GRAVITY OF SOLIDS**

The specific gravity of soil particles (G) is defined as the ratio of the mass of a given volume of solids to the mass of an equal 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) |