Soil Composition

Soil Composition

Learning Objectives

Understand the three-phase system of soil. - Define and calculate volumetric relationships such as void ratio, porosity, and degree of saturation. - Comprehend relative density and its application to coarse-grained soils. - Define weight relationships like water content and specific gravity. - Calculate unit weight relationships including moist, dry, saturated, and effective unit weights. - Utilize the fundamental "seven variables" relationship ( $Se = wG_s$ ) to solve phase relationship problems.

Soil is a complex particulate material consisting of three distinct phases: Solids (soil particles), Water (liquid), and Air (gas). The interactions and relative proportions of these phases determine the engineering properties of the soil, such as strength, compressibility, and permeability.

The Three-Phase System

To simplify calculations, soil is often represented as a Phase Diagram (or Block Diagram) that separates the three components by volume and weight.

Components of the Phase Diagram

Solids ( $V_s$ , $W_s$ ): The mineral particles forming the soil skeleton.
Water ( $V_w$ , $W_w$ ): The fluid filling the void spaces.
Air ( $V_a$ , $W_a \approx 0$ ): The gas filling the remaining voids.

Fundamental Definitions:

Total Volume ( $V_t$ ) = $V_s + V_w + V_a$
Volume of Voids ( $V_v$ ) = $V_w + V_a$
Total Weight ( $W_t$ ) = $W_s + W_w$ (Weight of air is negligible)

Interactive Phase Diagram

Interactive Phase Diagram

Adjust the volumes below to see how they affect the Void Ratio, Porosity, and Degree of Saturation.

Soil Phase Diagram (Three-Phase System)

Input Parameters

Volume of Solids (Vs)1.00

Volume of Water (Vw)0.50

Volume of Air (Va)0.20

Specific Gravity (Gs)2.65

Adjusting volumes changes the Void Ratio ( $e$ ) and Porosity ( $n$ ). Adjusting water changes Saturation ( $S$ ) and Water Content ( $w$ ).

Calculated Ratios

Void Ratio (e)Vv / Vs

0.700

Porosity (n)Vv / Vt

41.2%

Degree of Saturation (S)Vw / Vv

71.4%

Water Content (w)Ww / Ws

18.9%

Unit Weights (kN/m³)

Moist Unit Wt (γ)

18.18

Dry Unit Wt (γd)

15.29

Saturated Unit Wt (γsat)

19.33

Volumetric Relationships

These parameters describe the relative amount of voids in the soil mass.

Void Ratio ( $e$ )

The ratio of the volume of voids to the volume of solids. It is a measure of the packing density of the soil.

Range: $0 < e < \infty$
Typical Values for Sands: $0.4 - 0.8$
Typical Values for Clays: $0.6 - 1.5$ (can be $> 2$ for soft clays)

Void Ratio Formula

Ratio of the volume of voids to the volume of solids; a key measure of soil compactness.

e = \frac{V_v}{V_s}

Variables

Symbol	Description	Unit
$e$	Void ratio	unitless
$V_v$	Volume of voids	m³ or ft³
$V_s$	Volume of solids	m³ or ft³

Porosity ( $n$ )

The ratio of the volume of voids to the total volume, expressed as a percentage.

Range: $0 < n < 100\%$

Porosity Formula

Ratio of void volume to total volume, expressed as a percentage.

n = \frac{V_v}{V_t} \times 100\%

Variables

Symbol	Description	Unit
$n$	Porosity	%
$V_v$	Volume of voids	m³ or ft³
$V_t$	Total volume	m³ or ft³

Relationship between Void Ratio and Porosity

The following formulas relate void ratio to porosity directly.

Porosity from Void Ratio Formula

Converts void ratio to porosity directly.

n = \frac{e}{1+e}

Variables

Symbol	Description	Unit
$n$	Porosity	decimal or %
$e$	Void ratio	unitless

Void Ratio from Porosity Formula

Converts porosity to void ratio directly.

e = \frac{n}{1-n}

Variables

Symbol	Description	Unit
$e$	Void ratio	unitless
$n$	Porosity	decimal

Degree of Saturation ( $S$ )

The ratio of the volume of water to the volume of voids, expressed as a percentage.

Dry Soil: $S = 0\%$
Saturated Soil: $S = 100\%$
Partially Saturated: $0\% < S < 100\%$

Degree of Saturation Formula

Ratio of water volume to total void volume; indicates how much of the void space is filled with water.

S = \frac{V_w}{V_v} \times 100\%

Variables

Symbol	Description	Unit
$S$	Degree of saturation	%
$V_w$	Volume of water	m³ or ft³
$V_v$	Volume of voids	m³ or ft³

Relative Density ( $D_r$ )

A measure of the actual void ratio ( $e$ ) of a granular soil (sand or gravel) relative to its loosest ( $e_{max}$ ) and densest ( $e_{min}$ ) possible states. It is critical for assessing the strength, compressibility, and liquefaction potential of coarse-grained soils.

Very Loose: $D_r < 15\%$
Medium Dense: $35\% \le D_r < 65\%$
Very Dense: $D_r \ge 85\%$

Relative Density (Void Ratio) Formula

Quantifies the packing state of granular soils relative to their loosest and densest possible states, expressed using void ratios.

D_r = \frac{e_{max} - e}{e_{max} - e_{min}} \times 100\%

Variables

Symbol	Description	Unit
$D_r$	Relative density	%
$e$	In-situ void ratio	unitless
$e_{max}$	Maximum void ratio (loosest state)	unitless
$e_{min}$	Minimum void ratio (densest state)	unitless

Relative Density (Unit Weight)

Relative density can also be expressed in terms of dry unit weight ( $\gamma_d$ ):

Relative Density (Unit Weight) Formula

Alternative form of relative density expressed in terms of measured dry unit weights from field and lab tests.

D_r = \frac{\gamma_{d(field)} - \gamma_{d(min)}}{\gamma_{d(max)} - \gamma_{d(min)}} \times \left( \frac{\gamma_{d(max)}}{\gamma_{d(field)}} \right) \times 100\%

Variables

Symbol	Description	Unit
$D_r$	Relative density	%
$\gamma_{d(field)}$	In-situ dry unit weight	kN/m³ or pcf
$\gamma_{d(max)}$	Maximum dry unit weight (densest state)	kN/m³ or pcf
$\gamma_{d(min)}$	Minimum dry unit weight (loosest state)	kN/m³ or pcf

Weight Relationships

Water Content ( $w$ )

The ratio of the weight of water to the weight of solids, expressed as a percentage. Also known as moisture content.

Range: $w \ge 0\%$
Can exceed 100% for organic soils and sensitive clays (meaning weight of water > weight of solids).

Water Content Formula

Ratio of the weight of water to the weight of solids, expressed as a percentage; also called moisture content.

w = \frac{W_w}{W_s} \times 100\%

Variables

Symbol	Description	Unit
$w$	Water content	%
$W_w$	Weight of water	kN or lb
$W_s$	Weight of solids	kN or lb

Specific Gravity ( $G_s$ )

The ratio of the unit weight of soil solids to the unit weight of water.

Typical Values for Sand: 2.65
Typical Values for Clay: 2.70
Typical Values for Organic Soil: $< 2.0$

Specific Gravity Formula

Ratio of the unit weight of soil solids to the unit weight of water; typically around 2.65–2.70 for most minerals.

G_s = \frac{\gamma_s}{\gamma_w} = \frac{W_s}{V_s \gamma_w}

Variables

Symbol	Description	Unit
$G_s$	Specific gravity	unitless
$\gamma_s$	Unit weight of soil solids	kN/m³ or pcf
$\gamma_w$	Unit weight of water	kN/m³ or pcf
$W_s$	Weight of solids	kN or lb
$V_s$	Volume of solids	m³ or ft³

Unit Weight Relationships

Unit weight (or density) is the weight per unit volume. The following formulas calculate common unit weights for soils.

Moist (Bulk) Unit Weight Formula

Weight of soil per unit total volume at a given moisture content; the standard field unit weight.

\gamma = \frac{W_t}{V_t} = \frac{(G_s + Se)\gamma_w}{1+e} = \frac{(1+w)G_s \gamma_w}{1+e}

Variables

Symbol	Description	Unit
$\gamma$	Moist unit weight	kN/m³ or pcf
$W_t$	Total weight	kN or lb
$V_t$	Total volume	m³ or ft³
$G_s$	Specific gravity	unitless
$S$	Degree of saturation	decimal
$e$	Void ratio	unitless
$w$	Water content	decimal
$\gamma_w$	Unit weight of water	kN/m³ or pcf

Dry Unit Weight Formula

Used for compaction control.

\gamma_d = \frac{W_s}{V_t} = \frac{G_s \gamma_w}{1+e} = \frac{\gamma}{1+w}

Variables

Symbol	Description	Unit
$\gamma_d$	Dry unit weight	kN/m³ or pcf
$W_s$	Weight of solids	kN or lb
$V_t$	Total volume	m³ or ft³
$G_s$	Specific gravity	unitless
$\gamma_w$	Unit weight of water	kN/m³ or pcf
$e$	Void ratio	unitless
$\gamma$	Moist unit weight	kN/m³ or pcf
$w$	Water content	decimal

Saturated Unit Weight Formula

Calculated when S = 100% (or S = 1.0).

\gamma_{sat} = \frac{(G_s + e)\gamma_w}{1+e}

Variables

Symbol	Description	Unit
$\gamma_{sat}$	Saturated unit weight	kN/m³ or pcf
$G_s$	Specific gravity	unitless
$e$	Void ratio	unitless
$\gamma_w$	Unit weight of water	kN/m³ or pcf

Effective (Submerged) Unit Weight Formula

Unit weight of soil submerged below the water table, accounting for buoyancy; used in effective stress calculations.

\gamma' = \gamma_{sat} - \gamma_w = \frac{(G_s - 1)\gamma_w}{1+e}

Variables

Symbol	Description	Unit
$\gamma'$	Effective unit weight	kN/m³ or pcf
$\gamma_{sat}$	Saturated unit weight	kN/m³ or pcf
$\gamma_w$	Unit weight of water	kN/m³ or pcf
$G_s$	Specific gravity	unitless
$e$	Void ratio	unitless

Fundamental Relationship

The 'Seven' Variables Relationship

A crucial mnemonic to remember the relationship between Saturation, Void Ratio, Water Content, and Specific Gravity.

Basic Phase Relationship Formula

Useful for solving almost any phase relationship problem.

Se = wG_s

Variables

Symbol	Description	Unit
$S$	Degree of saturation	decimal
$e$	Void ratio	unitless
$w$	Water content	decimal
$G_s$	Specific gravity	unitless

Key Takeaways

Soil consists of Solids, Water, and Air. The Phase Diagram helps visualize these components.
Void Ratio ( $e$ ) and Porosity ( $n$ ) measure the volume of void space relative to solids or total volume, respectively.
Relative Density ( $D_r$ ) defines the packing state (loose vs. dense) of granular soils, crucial for assessing stability.
Degree of Saturation ( $S$ ) indicates how much of the void space is filled with water.
Unit Weights ( $\gamma, \gamma_d, \gamma_{sat}$ ) relate the weight of the soil to its volume and are critical for stress calculations.
The equation $Se = wG_s$ is the most powerful tool for solving phase relationship problems.

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Learning Objectives

The Three-Phase System

Components of the Phase Diagram

Interactive Phase Diagram

Interactive Phase Diagram

Soil Phase Diagram (Three-Phase System)

Input Parameters

Calculated Ratios

Unit Weights (kN/m³)

Volumetric Relationships

Void Ratio (eee)

Void Ratio Formula

Porosity (nnn)

Porosity Formula

Relationship between Void Ratio and Porosity

Porosity from Void Ratio Formula

Void Ratio from Porosity Formula

Degree of Saturation (SSS)

Degree of Saturation Formula

Relative Density (DrD_rDr​)

Relative Density (Void Ratio) Formula

Relative Density (Unit Weight)

Relative Density (Unit Weight) Formula

Weight Relationships

Water Content (www)

Water Content Formula

Specific Gravity (GsG_sGs​)

Specific Gravity Formula

Unit Weight Relationships

Moist (Bulk) Unit Weight Formula

Dry Unit Weight Formula

Saturated Unit Weight Formula

Effective (Submerged) Unit Weight Formula

Fundamental Relationship

The 'Seven' Variables Relationship

Basic Phase Relationship Formula

Void Ratio ( $e$ )

Porosity ( $n$ )

Degree of Saturation ( $S$ )

Relative Density ( $D_r$ )

Water Content ( $w$ )

Specific Gravity ( $G_s$ )