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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.

VOLUMETRIC RELATIONSHIPS

    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.

    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.

    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.

    Percentage air voids

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

    na= Va/V

    It is also expressed as a percentage.

    Air content

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

    ac= Va/Vv

    Also,

    na=n ac

    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.

    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 (ρd) is defined as the mass of solids per unit total volume

    ρd= Ms/V

    3. SATURATED MASS DENSITY

    The saturated mass density (ρsat) is the bulk density of the soil when it is fully saturated

    ρsat= 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 (ρs) is equal to the ratio of the mass of solids to the volume of solids

    ρs=Ms/Vs

    VOLUME-WEIGHT RELATIONSHIPS

  1. BULK UNIT WEIGHT (γ)= W/V
  2. DRY UNIT WEIGHT (γd) = Ws/V
  3. SATURATED UNIT WEIGHT (γsat) = Wsat/V
  4. SUBMERGED UNIT WEIGHT (γsub or γ’) = Wsub/V
  5. UNIT WEIGHT OF SOIL SOLIDS (γs) = Ws/Vs

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 = ρsw

The mass density of water ρw at 4°C is 1gm/ml, 1000 kg/m3 or 1 Mg/m3

BASIC RELATIONSHIPS

Sl NoRelationship in mass densityRelationship in unit weight
1n = e/(1+e)n = e/(1+e)
2e = n/(1-n)e = n/(1-n)
3na = n acna = n ac
4ρ= (G+Se)ρw/(1+e)γ= (G+Se) γ w/(1+e)
5ρd = Gρw/(1+e)γd = G γ w/(1+e)
6ρsat = (G+e)ρw/(1+e)γsat = (G+e) γ w/(1+e)
7ρ’ = (G-1)ρw/(1+e)γ’ = (G-1) γ w/(1+e)
8e = wG/se = wG/s
9ρd = ρ/(1+w)γd = γ/(1+w)
10ρd = (1-na)G ρw/(1+wG)γd = (1-na)G γ w/(1+wG)

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