Section 4: Soil and Water Conservation Engineering
Soil Physical Properties & Phase Relationships
Subtopic: Dry unit weight from moisture content and degree of saturation
Question Statement:
A soil specimen has a specific gravity of soil solids $G_s = 2.65$, gravimetric water content $w = 21.0\%$, and degree of saturation $S_r = 80\%$. Taking unit weight of water $\gamma_w = 9.81\text{ kN/m}^3$, the dry unit weight of the soil $\gamma_d$ is ________ $\text{kN/m}^3$ (round off to two decimal places).
Answer Key:
15.33
Step-by-Step Solution & Explanation
From the fundamental phase identity $e \cdot S_r = w \cdot G_s$:
$e = \frac{w G_s}{S_r} = \frac{0.210 \times 2.65}{0.8} = 0.6960$
Then, dry unit weight is:
$\gamma_d = \frac{G_s \gamma_w}{1 + e} = \frac{2.65 \times 9.81}{1 + 0.6960} = \frac{25.997}{1.6960} = 15.33\text{ kN/m}^3$.