Phase Diagram and Some Important Definitions

•  Phase Diagram and Some Important Definitions

Phase Diagram:-

• Phase diagram is a graphical representation of the physical state of Soil (any substance) under different conditions.
• Soil consists of solid particles with voids between particles filled with air, water, or both.
• These three constituents (solid particle, water and air) blended together to form soil.
• Constituents cannot be separated actually.
•  A 3-phase diagram is used for easy to understand and convenience in the calculation.
• Soil is a 3-phase system when it is partially saturated.
• It becomes a two-phase system when it is fully saturated or fully dry.
• In phase diagram constituents are arranged according to its specific gravity. Constituent with high specific gravity put in the lower position.

                                                               Fig.1- Three-Phase System

                                                                  Fig.2- Two-Phase System

Where-

V_A = Volume of Air

V_W = Volume of Water

V_S = Volume of Solid

V = Total volume of soil

V_V = Volume of Void

W_A = Weight of Air

W_W = Weight of Water

W_S = Weight of Solid

W = Total weight of soil

Some Important Definitions:-

Water Content:-

•  It is denoted by w.
•  It is also called moisture content.
•  It is the ratio of the weight of water to the weight of soil solids.

•  It expresses in percentage.
•  It has a minimum value of zero.
• There is no upper limit of Water content.
•  Fine drained soil has higher water content as compared to coarse-grained soil.
• It represents Hygroscopic water, Gravity water and Capillary water.
• It can be removed by oven drying.

Void Ratio:-

•  It is donated by e.
• It is the ratio of the volume of voids to the volume of solids.

• It expresses in decimal.
• It is always greater than zero.
• There is no upper limit of void ratio.
• It is a measure of Denseness (or Looseness) of soil.
• Size of void in coarse-grained soil is larger than that in fine-grained soil.
• Fine-grained soil has higher void ratio as compared to coarse-grained soil.
• Total volume of void in fine-grained soil is more as compared to coarse-grained soil.
• Void ratio is more important engineering property.

Porosity:-

• It is denoted by n.
• It is the ratio of the volume of voids to the total volume of the soil.

• It is expressed in percentage.
• The porosity of soil always less than 100%.
• It is always greater than zero.
• Porosity is also a measure of Denseness (or Looseness) of soil
• In comparison to porosity, the void ratio is more frequently used because the volume of solid remains constant, whereas total volume changes.

Degree of Saturation:-

• It is denoted by S.
• It is the ratio of the volume of water in the void to the volume of voids.

• It is expressed in percentage.
• The volume of voids is equal to the volume of air plus the volume of water in the soil mass.
• It has a maximum volume of 100%.
• It has a minimum value of 0%.
• For fully dry soil V_w = 0, Hence degree of saturation S = 0%.
• For fully saturated soil V_v = V_w, Hence degree of saturation S = 100%.
• For partially saturated soil, degree of saturation varies from 0 to 100%.

Air Content:-

• It is denoted by a_c.
• It is the ratio of the volume of air void to the total volume of voids.

• It is expressed in percentage.
• a_c = 1 – S

Percentage Air Voids:-

• It is denoted by n_a.
• It is the ratio of the volume of air voids to the total volume of the soil mass.

• It is expressed in percentage.
• n_a = n.a_c

Unit Weight:

Bulk Unit Weight:-

• It is denoted by γ_t.
• Bulk unit weight of soil mass is defined as total weight per unit volume of soil.
• It is the ratio of the total weight of the soil to the total volume of the soil.

• It is expressed as KN/m³, N/m³, kgf/cm³.

Unit Weight of Solids:-

• It is denoted by γ_s.
• It is also called Absolute unit weight.
• It represents the weight of soil solid per unit volume of solids.
• It is the ratio of the weight of soil solids to the total volume of the solids only (soil solid).

Unit Weight of Water:-

• It is denoted by γ_w.
• It is the weight per unit volume of water.
• It is the ratio of the weight of water to the volume of the water.

• The value of the unit weight of water changes with the temperature of the water.
• The unit weight of water usually taken as 9.81 KN/m³ or 1000 Kg/m³ at 4⁰C.

Dry Unit Weight:-

• It is denoted by γ_d.
• It represents the weight of soil solid or weight of dry soil per unit volume of the soil mass.
• It is the ratio of the weight of dry soil or weight of soil solids to the total volume of the soil mass.

• It is a measure of the denseness of soil.
• Higher the value of dry unit weight represents the more compacted soil.

Saturated Unit Weight:-

• It is denoted by γ_sat.
• It represents the bulk unit weight of the soil in a saturated condition.
• It is the ratio of the weight of soil in saturated condition (weight of saturated soil) to the total volume of the soil mass. 

γ_{sat =} W_{sat / V}

Submerged Unit Weight:-

• It is denoted by γ_sub or It is denoted by γʹ.
• It is also called Buoyant unit weight.
• It represents the unit weight of soil in submerged condition.
• It is the ratio of the weight of soil in submerged condition or weight of submerged soil to the total volume of soil.
• A buoyant force acts on the soil solids when soil exists below ground level i.e. in submersed condition; this buoyant force reduces the unit weight of soil.
• Soil in submerged condition will be in saturated state also, but soil in saturated condition need not to be submerged.
• Soil below water table is in submerged as well as saturated condition.
• Soil in capillary zone is in saturated condition only.
• γʹ = γ_sat - γ_w
• Generally γʹ = 0.5×γ_sat

Note:-

           Order of unit weight of soil-

                           γ_s > γ_sat > γ_t > γ_d > γ_sub

Specific Gravity:

Specific Gravity of Solid:-

• It is denoted by G.
• It is also called True Specific Gravity or Absolute Specific Gravity or Grain Specific Gravity.
• It is defined as the ratio of unit weight of soil solids to the unit weight of water at 4⁰C.

• It is unitless quantity.
• The specific gravity of fine-grained soil is always greater than the specific gravity of coarse-grained soil (G_{fine grained soil} > G_{coarse grained soil}).
• The specific gravity of soil is directly proportional to the Mineral content, like- Iron + Mica. (G α Mineral content)
• The specific gravity of soil is inversely proportional to the amount of organic matter content. (G α 1/Amount of organic matter content).
• G = 1.2 to 1.4 for organic soil.

            = 2.6 to 2.75 for inorganic soil.

• In India, specific gravity is reported at 27⁰C,

Mass Specific Gravity:-

• It is denoted by G_m.
• It is also called Apparent specific gravity.
• It is defined as the ratio of unit weight of soil mass in natural state (i.e. γ_sat or γ_t or γ_d ) to the unit weight of water.

• It is a unitless quantity.
• Mass specific gravity is always less than Specific gravity (G_m < G).
•  G_m = G / (1+e)

Relative density (D_r) or Density Index (I_D):-

• It is used to compare the degree of denseness of two cohesionless soils.

• When particles are arranged in cubical array-

          e_max = 0.91 = Void ratio of soil in densest state

• When particles are arranged in prismoidal array-

          e_min = 0.35 = Void ratio of soil in loosest state

• This parameter is used in sandy and gravelly soils.
• Loose soil has a low value of relative density, whereas dense soil has a high value of relative density.
• Relative density is directly proportional to the shear strength of soil.

Relative density α shear strength of soil

• Relative density is inversely proportional to the compressibility of soil.

Relative density α 1/Compressibility of soil

• The lowest possible value of Relative density is 0.
• The highest possible value of Relative density is 100.
• According to relative density, the soil is classified as-

Relative density	Classification
0-15	Very loose soil
15-30	Loose soil
30-65	Medium dense soil
65-85	Dense soil
85-100	Very dense soil

 Relative Compaction:-

• It is denoted by R_c.
• It is used to compare the degree of denseness of two cohesive and cohesionless soils both.

                                                        R_c= γ_D / γ_Dmax