Three Phase Diagram in Soil Mechanics – Part 3 Void Ratio, Porosity and Soil Properties Soil Mechanics-I | Module-1 | MAKAUT Civil Engineering

Three Phase Diagram in Soil Mechanics – Part 3

Void Ratio, Porosity and Soil Properties

Soil Mechanics-I | Module-1 | MAKAUT Civil Engineering

Soil is a naturally occurring material composed of solid particles with void spaces between them. These void spaces may contain water, air, or both. To study the engineering behavior of soil, geotechnical engineers represent soil as a three-phase system consisting of solids, water, and air.

The concept of the three-phase system is fundamental in Soil Mechanics because many important engineering properties such as void ratio, porosity, degree of saturation, water content, and unit weight are derived from it. Understanding these relationships is essential for solving numerical problems and analyzing soil behavior in field conditions.

Three Phase System of Soil

A soil mass consists of three components:

1. Solid Phase

The solid phase consists of mineral particles formed from the weathering of rocks.

• Sand
• Silt
• Clay
• Gravel

The volume occupied by soil particles is represented by Vs and the weight of solids is represented by Ws.

2. Water Phase

The void spaces between soil particles may contain water.

The volume of water is represented by Vw and its weight by Ww.

Water greatly affects the engineering behavior of soil.

3. Air Phase

The remaining void spaces not occupied by water contain air.

The volume of air is represented by Va.

The weight of air is generally neglected because it is extremely small compared to the weight of soil solids and water.

Volume Relationships

The total volume of soil is the sum of the volume of solids and the volume of voids.

V = Vs + Vv

where

Vv = Vw + Va

Therefore,

V = Vs + Vw + Va

Weight Relationships

The total weight of soil is:

W = Ws + Ww

Since the weight of air is negligible:

Wa = 0

Therefore,

W = Ws + Ww

Void Ratio (e)

Definition

Void ratio is defined as the ratio of the volume of voids to the volume of solids present in a soil mass.

It is represented by the symbol e.

Formula

e = Vv / Vs

Where:

• Vv = Volume of voids
• Vs = Volume of solids

Explanation

Void ratio indicates how much empty space exists in a soil relative to the amount of solid material.

A larger void ratio means more void space and a looser soil structure. A smaller void ratio means less void space and a denser soil structure.

Engineering Significance of Void Ratio

• Indicates soil density and compactness.
• Helps in settlement analysis.
• Influences shear strength of soil.
• Affects permeability and drainage characteristics.
• Used extensively in geotechnical design calculations.

Typical Values of Void Ratio

Soil Type	Void Ratio
Dense Sand	0.30 – 0.60
Loose Sand	0.60 – 1.00
Clay	0.50 – 2.00
Organic Soil	Greater than 2.00

Porosity (n)

Definition

Porosity is defined as the ratio of the volume of voids to the total volume of soil.

It is represented by the symbol n.

Formula

n = (Vv / V) × 100%

Where:

• Vv = Volume of voids
• V = Total volume of soil

Explanation

Porosity represents the percentage of the total soil volume occupied by voids. These void spaces may contain water, air, or both.

Higher porosity means greater storage capacity for water and air, while lower porosity indicates a denser soil structure.

Engineering Significance of Porosity

• Controls groundwater storage.
• Influences drainage and seepage.
• Affects soil aeration.
• Important for agricultural and engineering applications.
• Determines water-holding capacity of soil.

Relationship Between Void Ratio and Porosity

One of the most important relationships in Soil Mechanics is the connection between void ratio and porosity.

Formula

n = e / (1 + e)

and

e = n / (1 − n)

Importance

• Frequently asked in MAKAUT examinations.
• Useful for solving numerical problems.
• Helps convert one parameter into another.

Comparison Between Void Ratio and Porosity

Void Ratio	Porosity
Ratio of void volume to solid volume	Ratio of void volume to total volume
Represented by e	Represented by n
Can be greater than 1	Always less than 100%
Dimensionless quantity	Usually expressed in percentage

Water Content (w)

Definition

Water content is the ratio of the weight of water to the weight of soil solids.

Formula

w = (Ww / Ws) × 100%

Importance

• Indicates moisture condition of soil.
• Affects strength and compressibility.
• Essential in compaction studies.
• Used in laboratory testing.

Degree of Saturation (S)

Definition

Degree of saturation is the ratio of the volume of water to the volume of voids.

Formula

S = (Vw / Vv) × 100%

Interpretation

• S = 0% → Completely dry soil.
• S = 100% → Fully saturated soil.

Air Content

Air content is the ratio of the volume of air to the volume of voids.

a = (Va / Vv) × 100%

Unit Weight of Soil (γ)

Definition

Unit weight is the weight per unit volume of soil.

Formula

γ = W / V

Unit: kN/m³

Dry Unit Weight (γd)

Definition

Dry unit weight is the weight of soil solids per unit total volume.

Formula

γd = Ws / V

Importance

Dry unit weight is widely used in compaction control and field density testing.

Saturated Unit Weight (γsat)

When all void spaces are completely filled with water, the soil reaches a saturated condition.

The corresponding unit weight is called the Saturated Unit Weight (γsat).

Submerged Unit Weight (γ')

For soils below the groundwater table:

γ' = γsat − γw

Where γw = 9.81 kN/m³.

Practical Engineering Applications

• Foundation Engineering
• Highway Engineering
• Earth Dams
• Retaining Structures
• Groundwater Engineering
• Geotechnical Investigation
• Compaction and Quality Control

Important Examination Formulas

e = Vv / Vs

n = (Vv / V) × 100%

n = e / (1 + e)

e = n / (1 − n)

w = (Ww / Ws) × 100%

S = (Vw / Vv) × 100%

γ = W / V

γd = Ws / V

Conclusion

The Three Phase System is the foundation of Soil Mechanics. Concepts such as void ratio, porosity, water content, degree of saturation, and unit weight help engineers understand the behavior of soil under various field conditions. A strong understanding of these relationships is essential for solving numerical problems, analyzing soil properties, and designing safe civil engineering structures.