Question

A uniformly distributed line load of 500 kN/m is acting on the ground surface based on Boussinesq’s theory, the ratio of vertical stress at a depth 2 m to that at 4 m right below the limit of loading is
1. 0.25
2. 0.5
3. 2.0
4. 4.0

Answer 1

Correct Answer - Option 3 : 2.0

Due to uniformly distributed line load vertical stress

\(= \frac{{2q}}{{\pi z}}{\left[ {\frac{1}{{1 + {{\left( {\frac{x}{z}} \right)}^2}}}} \right]^2}\)

Vertically below line load x = 0

\(\begin{array}{l} {\sigma _z} = \frac{{2q}}{{\pi z}}\\ \frac{{{\sigma _1}}}{{{\sigma _2}}} = \frac{{{z_2}}}{{{z_1}}} = \frac{4}{2} = 2 \end{array}\)