Density Parameters
Bulk Density of Soil or Moist Density is the total mass, M of the soil per unit of its total volume, V. Thus, ρ = M/V
Dry Density is the mass of solids (Md) per unit of total volume (prior to drying) of the soil mass. Thus, ρd = Md/V
The density of Solids is the mass of soil solids (Md) per unit of volume of solids (Vs). Thus, ρs = Md/Vs
Saturated Density (ρsat) is the bulk density of the soil when it is saturated. It is the ratio of the total soil mass (M) of a saturated sample to its total volume, V.
Submerged Density (ρ1) is the submerged mass of soil solids (Md)sub per unit of total volume, V of the soil mass. Thus, ρ1= (Md)sub/V. Submerged density is also known as buoyant density, ρ1 = ρsat – ρw, where, ρw = density of water (usually taken as 1000 kg/m3 or 1 g/cm3 for calculation purposes).
Other Function Relationships
ρd = [(G. ρw)/ (1 + e)] or [(1 – n) G. ρw] or [ρ/ (1 + w)]
ρsat = [(G + e) ρw / (1 + e)] or [G – ρw / (1 – n)]
ρ = (G + eS) ρw / (1 + e)
ρ1 = (G – 1) ρw / (1 + e)
Where,
S = degree of saturation of soil
e = void ratio (Volume of voids, Vv)/ (Volume of solids, Vs) or wG/S
n = porosity (Volume of voids, Vv)/ (Total volume, V)
G = specific gravity of soil
w = moisture content of the soil
Unit Weight Parameters
The unit Weight of soil mass is defined as its weight (W) per unit volume (V).
Bulk Unit Weight (𝛾) or moist unit weight is the total weight, W of a soil mass per unit of its total volume, V. Thus, 𝛾 = w/V
Dry Unit Weight (𝛾d) is the weight of solids (Wd) per unit of its total volume, V (before drying). Thus, 𝛾d = Wd/V
Unit Weight of Solids (𝛾s) is the weight of soil solids (Wd) per unit volume of solids (Vs). Thus, 𝛾s = Wd/Vs
Note: since the volume of solids, Vs does not alter, 𝛾s is constant for a given soil whereas 𝛾d varies because it depends on the total volume of soil mass, V.
Saturated Unit Weight (𝛾sat) is the bulk unit weight of the soil when it is saturated. It is the ratio of the total weight of the soil sample to its total volume when the soil is saturated.
Submerged Unit Weight (𝛾1) is the submerged weight of solids (Wd)sub per unit of total volume, V of the soil mass. Thus, 𝛾1 = (Wd)sub/V. When the soil mass is submerged, 𝛾1 = 𝛾sat – 𝛾w, where 𝛾w is the unit weight of water (usually 10 kN/m3).
Other Functional Relationships
S = (w. G)/e
na (% air voids) = e (1 – S)/ (1 + e)
𝛾d = [(G. 𝛾w)/ (1 + e)] or [(1 – n) G. 𝛾w]
𝛾sat = [(G + e) 𝛾w / (1 + e)] or [G – 𝛾w / (1 – n)]
𝛾 = (G + eS) 𝛾w / (1 + e)
𝛾1 = (G – 1) 𝛾w / (1 + e)
Where,
S = degree of saturation of soil
e = void ratio (Volume of voids, Vv)/ (Volume of solids, Vs)
n = porosity (Volume of voids, Vv)/ (Total volume, V)
G = specific gravity of soil
w = moisture content of the soil
