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COMPLETE SOIL FORMULAS
Soil is composed of solids, liquids, and gases. Liquids and gases are mostly water and
air, respectively. These two (water and air) are called voids which occupy between soil
particles. The figure shown below is an idealized soil drawn into phases of solids, water,
and air.
Weight-Volume Relationship from the Phase Diagram of Soil
total volume = volume of soilds + volume of voids
volume of voids = volume of water + volume of air
total weight = weight of solids + weight of water
Soil Properties
Void Ratio, e
Void ratio is the ratio of volume of voids to the volume of solids.
Porosity, n
Porosity is the ratio of volume of voids to the total volume of soil.
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Degree of Saturation, S
Degree of saturation is the ratio of volume of water to the volume of voids.
Water Content or Moisture Content, w
Moisture content, usually expressed in terms of percentage, is the ratio of the weight of
water to the weight of solids.
Unit Weight, γ
Unit weight is the weight of soil per unit volume. Also called bulk unit weight (γ), and
moist unit weight (γ
m
).
Dry Unit Weight, γ
d
Dry unit weight is the weight of dry soil per unit volume.
Saturated Unit Weight, γ
sat
Saturated unit weight is the weight of saturated soil per unit volume.
Effective Unit Weight, γ'
Effective unit weight is the weight of solids in a submerged soil per unit volume. Also
called buoyant density or buoyant unit weight (γ
b
).
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Specific Gravity of Solid Particles, G
Specific gravity of solid particles of soil is the ratio of the unit weight of solids (γ
s
) to the
unit weight of water (γ
w
).
Formulas for Properties of Soil
Symbols and Notations
= void ratio
= porosity
= moisture content, water content
= specific gravity of any substance
= specific gravity of solids
= degree of saturation
= volume of soil mass
= volume of air
= volume of water
= volume of solids
= volume of voids
= total weight of soil
= weight of water
= weight of solids
= relative density
= unit weight of soil mass, moist unit weight, bulk unit weight
= unit weight of soil solids
= unit weight of water
= = buoyant unit weight, submerged unit weight
= = dry unit weight
= saturated unit weight
= liquid limit
= plastic limit
= liquidity index
= plasticity index
= group index
Basic Formulas
Unit weight,
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Weight,
Specific gravity,
Physical Properties of Soil
Total weight,
Total volume,
Volume of voids,
Void ratio, , Note:
Porosity, , Note:
Relationship between e and n, and
Water content or moisture content, , Note:
Degree of saturation, , Note:
Relationship between G, w, S, and e,
Moist unit weight or bulk unit weight,
, also or
Dry unit weight, and
Saturated unit weight,
Submerged or buoyant unit weight, or
Critical hydraulic gradient, or
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Relative Density, or
Atterberg Limits
Plasticity index,
Liquidity index,
Shrinkage index,
Activity of clay, , where = soil finer than 0.002 mm in percent
Other Formulas
Volume of voids,
Volume of solids,
Volume of water,
Weight of water,
Weight of soil,
Dry unit weight,
Relationship between specific gravity of
solids, moisture content, degree of
saturation, and void ratio
The relationship between , , , and is given by the following
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G = specific gravity of solid particles
w = moisture content or water content
S = degree of saturation
e = void ratio
The formula above can be derived as follows:
Thus, as stated above.
Relationship between void ratio and
porosity
The relationship between and is given by
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and
Derivation is as follows
void ratio
n = V
v
/ V
(okay!)
porosity
e = V
v
/ V
s
(okay!)
- See more at: http://www.mathalino.com/reviewer/geotechnical-engineering/physical-
properties-soil#sthash.puuibPl0.dpuf

Unformatted Attachment Preview

COMPLETE SOIL FORMULAS Soil is composed of solids, liquids, and gases. Liquids and gases are mostly water and air, respectively. These two (water and air) are called voids which occupy between soil particles. The figure shown below is an idealized soil drawn into phases of solids, water, and air. Weight-Volume Relationship from the Phase Diagram of Soil total volume = volume of soilds + volume of voids volume of voids = volume of water + volume of air total weight = weight of solids + weight of water Soil Properties Void Ratio, e Void ratio is the ratio of volume of voids to the volume of solids. Porosity, n Porosity is the ratio of volume of voids to the total volume of soil. Degree of Saturation, S Degree of saturation is the ratio of volume of water to the volume of voids. Water Content or Moisture Content, w Moisture content, usually expressed in terms of percentage, is the ratio of the weight of water to the weight of solids. Unit Weight, γ Unit weight is the weight of soil per unit volume. Also called bulk unit weight (γ), and moist unit weight (γm). Dry Unit Weight, γd Dry unit weight is the weight of dry soil per unit volume. Saturated Unit Weight, γsat Saturated unit weight is the weight of saturated soil per unit volume. Effective Unit Weight, γ' Effective unit weight is the weight of solids in a submerged soil per unit volume. Also called buoyant density or buoyant unit weight (γb). Specific Gravity of Solid Particles, G Specific gravity of solid particles of soil is the ratio of the unit weight of solids (γs) to the unit weight of water (γw). Formulas for Properties of Soil Symbols and Notations = void ratio = porosity = moisture content, water content = specific gravity of any substance = specific gravity of solids = degree of saturation = volume of soil mass = volume of air = volume of water = volume of solids = volume of voids = total weight of soil = weight of water = weight of solids = relative density = unit weight of soil mass, moist unit weight, bulk unit weight = unit weight of soil solids = unit weight of water = = buoyant unit weight, submerged unit weight = = dry unit weight = saturated unit weight = liquid limit = plastic limit = liquidity index = plasticity index = group index Basic Formulas Unit weight, Weight, Specific gravity, Physical Properties of Soil Total weight, Total volume, Volume of voids, Void ratio, , Porosity, , Note: Note: Relationship between e and n, and Water content or moisture content, Degree of saturation, , , Note: Relationship between G, w, S, and e, Moist unit weight or bulk unit weight, , also Dry unit weight, or and Saturated unit weight, Submerged or buoyant unit weight, Critical hydraulic gradient, or or Note: Relative Density, or Atterberg Limits Plasticity index, Liquidity index, Shrinkage index, Activity of clay, , where = soil finer than 0.002 mm in percent Other Formulas Volume of voids, Volume of solids, Volume of water, Weight of water, Weight of soil, Dry unit weight, Relationship between specific gravity of solids, moisture content, degree of saturation, and void ratio The relationship between , , , and is given by the following G = specific gravity of solid particles w = moisture content or water content S = degree of saturation e = void ratio The formula above can be derived as follows: Thus, as stated above. Relationship between void ratio and porosity The relationship between and is given by and Derivation is as follows → void ratio → n = Vv / V (okay!) → porosity → e = Vv / Vs (okay!) - See more at: http://www.mathalino.com/reviewer/geotechnical-engineering/physicalproperties-soil#sthash.puuibPl0.dpuf Name: Description: ...
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