Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Fundamental definitions and relationships
Question Statement:
A compacted soil sample has a void ratio of $e = 0.65$ and a specific gravity of soil solids $G_s = 2.68$. If the degree of saturation of the soil is $S_r = 75.0\%$, the gravimetric water content $w$ of the soil in percent ($\text{\%}$) is ________ (round off to two decimal places).
Answer Key:
18.19
Step-by-Step Solution & Explanation
**Method 1: Phase Relationship Equation**
From basic volumetric-gravimetric phase relations:
$S_r \cdot e = w \cdot G_s \implies w = \frac{S_r \cdot e}{G_s}$
Given:
- $S_r = 0.75$
- $e = 0.65$
- $G_s = 2.68$
$w = \frac{0.75 \times 0.65}{2.68} = \frac{0.4875}{2.68} = 0.181903 = 18.19\%$
**Method 2: Volume-Mass Balance Basis**
Assuming volume of solids $V_s = 1.0\text{ m}^3$:
- Mass of solids $M_s = G_s \rho_w V_s = 2.68 \times 1000 = 2680\text{ kg}$
- Volume of voids $V_v = e V_s = 0.65\text{ m}^3$
- Volume of water $V_w = S_r V_v = 0.75 \times 0.65 = 0.4875\text{ m}^3$
- Mass of water $M_w = \rho_w V_w = 487.5\text{ kg}$
- Water content $w = \frac{M_w}{M_s} = \frac{487.5}{2680} = 0.1819 = 18.19\%$