Soil Composition

Soil Composition

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

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.

Void Ratio

$$
e = \frac{V_v}{V_s}
$$

Porosity ( $n$ )

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

Porosity

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

Relationship between $e$ and $n$ :

Porosity from Void Ratio

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

Void Ratio from Porosity

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

Degree of Saturation ( $S$ )

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

Degree of Saturation

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

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.

Relative Density (Void Ratio)

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

It can also be expressed in terms of dry unit weight (

\gamma_d

Relative Density (Unit Weight)

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

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.

Water Content

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

Specific Gravity ( $G_s$ )

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

Specific Gravity

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

Unit Weight Relationships

Unit weight (or density) is the weight per unit volume.

Common Unit Weights

Moist (Bulk) Unit Weight

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

Dry Unit Weight

Used for compaction control.

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

Saturated Unit Weight

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

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

Effective (Submerged) Unit Weight

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

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

Useful for solving almost any phase relationship problem.

$$
Se = wG_s
$$

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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The Three-Phase System