To simplify calculations, soil is often represented as a phase diagram (block diagram) separating the three components:

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

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)

The ratio of the volume of voids to the volume of solids. $e = \frac{V_v}{V_s}$ Range: $0 < e < \infty$ (Typically 0.3 to 1.5 for natural soils)

The ratio of the volume of voids to the total volume. $n = \frac{V_v}{V_t} \times 100\%$ Range: $0\% < n < 100\%$

Relationship between $e$ and $n$: $n = \frac{e}{1+e}$ $e = \frac{n}{1-n}$

The ratio of the volume of water to the volume of voids. $S = \frac{V_w}{V_v} \times 100\%$

• Dry Soil: $S = 0\%$
• Saturated Soil: $S = 100\%$

The ratio of the weight of water to the weight of solids. Also known as moisture content. $w = \frac{W_w}{W_s} \times 100\%$ Range: $w \ge 0\%$

The ratio of the unit weight of soil solids to the unit weight of water. $G_s = \frac{\gamma_s}{\gamma_w} = \frac{W_s}{V_s \gamma_w}$ Typical values: 2.65 - 2.70 for sands/clays.

The weight per unit volume of soil. $\gamma = \frac{W_t}{V_t}$

Dry Unit Weight ($\gamma_d$): $\gamma_d = \frac{W_s}{V_t} = \frac{G_s \gamma_w}{1+e}$

Saturated Unit Weight ($\gamma_{sat}$) ($S=100\%$): $\gamma_{sat} = \frac{(G_s + e)\gamma_w}{1+e}$

Moist (Bulk) Unit Weight ($\gamma$): $\gamma = \frac{(G_s + Se)\gamma_w}{1+e}$

A mnemonic to remember the relationship between Saturation, Void Ratio, Water Content, and Specific Gravity: $Se = wG_s$