Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Terzaghi's one dimensional soil consolidation theory
Question Statement:
A point load of $500\text{ kN}$ acts on the ground surface. Using Boussinesq's theory, the vertical stress $\sigma_z$ directly below the load at a depth of $2.0\text{ m}$ in $\text{kPa}$ is ________ (round off to 1 decimal place).
Answer Key:
59.7
Step-by-Step Solution & Explanation
Boussinesq equation for vertical stress directly beneath a point load ($r = 0$):
$\sigma_z = \frac{3 Q}{2 \pi z^2}$
Given $Q = 500\text{ kN}$ and $z = 2.0\text{ m}$:
$\sigma_z = \frac{3 \times 500}{2 \pi \times (2.0)^2} = \frac{1500}{8 \pi} = \frac{1500}{25.1327} \approx 59.68\text{ kPa} \approx 59.7\text{ kPa}$